For a one-off it is probably easiest to force the name order of the full name with curly braces and fill the shortauthor field with just the family name.
\documentclass[american]{article}
\usepackage[T1]{fontenc}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[backend=biber, authordate]{biblatex-chicago}
\begin{filecontents}{\jobname.bib}
@article{Li:2018,
author = {{Li Wei}},
shortauthor = {Li},
date = {2018},
journaltitle = {Applied Linguistics},
number = {1},
pages = {9--30},
title = {Translanguaging as a Practical Theory of Language},
volume = {39},
}
@article{Li+Milroy:1995,
author = {{Li Wei} and Milroy, Lesley},
shortauthor = {Li and Milroy, Lesley},
date = {1995},
journaltitle = {Journal of Pragmatics},
number = {3},
pages = {281--299},
title = {Conversational Code-Switching in a {Chinese} Community in {Britain}:
A Sequential Analysis},
volume = {23},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\addbibresource{biblatex-examples.bib}
\begin{document}
Lorem \autocite{sigfridsson}
ipsum \autocite{Li:2018}
dolor \autocite{Li+Milroy:1995}
\printbibliography
\end{document}

For a more comprehensive treatment of non-Western names you can make use of biblatex's extended name format. As luck would have it, for east Asian names and biblatex-chicago this was already done in CJK Bibliography Problem, Biblatex-Chicago author-date style, so we can just copy the code.
The advantage of this approach is that you do not have to duplicate name data in the same entry and that all name disambiguation features continue to work as intended. The disadvantage is the arguably more clunky input format.
\documentclass[american]{article}
\usepackage[T1]{fontenc}
\usepackage{babel}
\usepackage{csquotes}
\begin{filecontents}{chicago-authordate.dbx}
\ProvidesFile{chicago-authordate.dbx}[2016/07/24 extended name format for biblatex]
\DeclareDatamodelConstant[type=list]{nameparts}{prefix,family,suffix,given,cjk}
\end{filecontents}
\usepackage[authordate,backend=biber]{biblatex-chicago}
\DeclareSortingNamekeyTemplate[cjk]{
\keypart{
\namepart{family}
}
\keypart{
\namepart{given}
}
\keypart{
\namepart{cjk}
}
}
\DeclareUniquenameTemplate[cjk]{
\namepart[base=true]{family}
\namepart[disambiguation=full]{given}
\namepart[disambiguation=full]{cjk}
}
\newbibmacro*{name:cjk}[3]{%
\usebibmacro{name:delim}{#2#3#1}%
\usebibmacro{name:hook}{#2#3#1}%
\mkbibnamefamily{#1}%
\ifdefvoid{#2}{}{\bibnamedelimd\mkbibnamegiven{#2}}%
\ifdefvoid{#3}{}{\bibnamedelimd\mkbibnamecjk{#3}}}
\newbibmacro{labelname:western}{%
\ifcase\value{uniquename}%
\usebibmacro{name:family}
{\namepartfamily}
{\namepartgiven}
{\namepartprefix}
{\namepartsuffix}%
\or
\ifuseprefix
{\usebibmacro{name:given-family}
{\namepartfamily}
{\namepartgiveni}
{\namepartprefix}
{\namepartsuffixi}}
{\usebibmacro{name:given-family}
{\namepartfamily}
{\namepartgiveni}
{\namepartprefixi}
{\namepartsuffixi}}%
\or
\usebibmacro{name:given-family}
{\namepartfamily}
{\namepartgiven}
{\namepartprefix}
{\namepartsuffix}%
\fi
\usebibmacro{name:andothers}}
\newbibmacro{labelname:cjk}{%
\iffieldequalstr{uniquepart}{base}%
{\usebibmacro{name:cjk}
{\namepartfamily}
{\empty}
{\empty}}
{\iffieldequalstr{uniquepart}{given}%
{\usebibmacro{name:cjk}
{\namepartfamily}
{\namepartgiven}
{\empty}}
{\usebibmacro{name:cjk}
{\namepartfamily}
{\namepartgiven}
{\namepartcjk}}}}
\DeclareNameFormat{labelname}{%
\ifuniquenametemplatename{cjk}
{\usebibmacro{labelname:cjk}}
{\usebibmacro{labelname:western}}%
\usebibmacro{name:andothers}}
\DeclareNameFormat{family-given}{%
\ifsortingnamekeytemplatename{cjk}
{\usebibmacro{name:cjk}{\namepartfamily}{\namepartgiven}{\namepartcjk}}
{\ifgiveninits
{\usebibmacro{name:family-given}
{\namepartfamily}
{\namepartgiveni}
{\namepartprefix}
{\namepartsuffix}}
{\usebibmacro{name:family-given}
{\namepartfamily}
{\namepartgiven}
{\namepartprefix}
{\namepartsuffix}}}%
\usebibmacro{name:andothers}}
\DeclareNameFormat{given-family}{%
\ifsortingnamekeytemplatename{cjk}
{\usebibmacro{name:cjk}{\namepartfamily}{\namepartgiven}{\namepartcjk}}
{\ifgiveninits
{\usebibmacro{name:given-family}
{\namepartfamily}
{\namepartgiveni}
{\namepartprefix}
{\namepartsuffix}}
{\usebibmacro{name:given-family}
{\namepartfamily}
{\namepartgiven}
{\namepartprefix}
{\namepartsuffix}}}%
\usebibmacro{name:andothers}}
\DeclareNameFormat{family-given/given-family}{%
\ifsortingnamekeytemplatename{cjk}
{\usebibmacro{name:cjk}{\namepartfamily}{\namepartgiven}{\namepartcjk}}
{\ifnumequal{\value{listcount}}{1}
{\ifgiveninits
{\usebibmacro{name:family-given}
{\namepartfamily}
{\namepartgiveni}
{\namepartprefix}
{\namepartsuffix}}
{\usebibmacro{name:family-given}
{\namepartfamily}
{\namepartgiven}
{\namepartprefix}
{\namepartsuffix}}
\ifboolexpe{%
test {\ifdefvoid\namepartgiven}
and
test {\ifdefvoid\namepartprefix}}
{}
{\usebibmacro{name:revsdelim}}}
{\ifgiveninits
{\usebibmacro{name:given-family}
{\namepartfamily}
{\namepartgiveni}
{\namepartprefix}
{\namepartsuffix}}
{\usebibmacro{name:given-family}
{\namepartfamily}
{\namepartgiven}
{\namepartprefix}
{\namepartsuffix}}}}
\usebibmacro{name:andothers}}
\begin{filecontents}{\jobname.bib}
@article{Li:2018,
author = {family=Li, given=Wei, nametemplates=cjk},
date = {2018},
journaltitle = {Applied Linguistics},
number = {1},
pages = {9--30},
title = {Translanguaging as a Practical Theory of Language},
volume = {39},
}
@article{Li+Milroy:1995,
author = {family=Li, given=Wei, nametemplates=cjk and Milroy, Lesley},
date = {1995},
journaltitle = {Journal of Pragmatics},
number = {3},
pages = {281--299},
title = {Conversational Code-Switching in a {Chinese} Community in {Britain}:
A Sequential Analysis},
volume = {23},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\addbibresource{biblatex-examples.bib}
\begin{document}
Lorem \autocite{sigfridsson}
ipsum \autocite{Li:2018}
dolor \autocite{Li+Milroy:1995}
\printbibliography
\end{document}

shortauthorsolution is certainly sufficient for my use-case but it's good to know that a more comprehensive solution exists as well. – jan Mar 04 '21 at 09:41