This is an attempt to talk you out of this. But let me start with an in principle working prototype example.
\documentclass{article}
\usepackage{environ}
\usepackage{tcolorbox,xcolor}
\newtcolorbox[blend into=tables]{tablebox}[1][]{%
float=htb,
sharp corners,
colback=blue!5,
colframe=blue!50!darkgray,
capture=hbox,every float=\centering,#1}
\makeatletter
\newsavebox\TabB@x
\newif\ifTab@hasTitle
\newif\ifTab@hasLabel
\tcbset{tab@title/.code={\ifTab@hasTitle
\tcbset{title=#1}%
\fi},tab@label/.code={\ifTab@hasLabel
\tcbset{label=#1}%
\fi}}
\NewEnviron{Table}[1][]{\begingroup
\gdef\@gtempa{\relax}%
\gdef\@gtempb{\relax}%
\global\Tab@hasTitlefalse
\global\Tab@hasLabelfalse
\renewcommand\caption[1]{\global\Tab@hasTitletrue\gdef\@gtempa{##1}}%
\renewcommand\label[1]{\global\Tab@hasLabeltrue\gdef\@gtempb{##1}}%
\begin{lrbox}\TabB@x
\BODY
\end{lrbox}%
\global\setbox\TabB@x\box\TabB@x
\endgroup
\begin{tablebox}[tab@title=\@gtempa, tab@label=\@gtempb,code={\par\medskip}]
\usebox\TabB@x
\end{tablebox}}
\makeatother
\begin{document}
Table \ref{temperatures} uses a tcolorbox.
\begin{Table}
\caption{My table}
\label{temperatures}
%\begin{center}
\begin{tabular}{ll}
\hline
Paris & 21 degrees\\
Berlin & 19 degrees\\
\hline
\end{tabular}
%\end{center}
\end{Table}
Table \ref{lowtemperatures} has no title.
\begin{Table}
\label{lowtemperatures}
\begin{tabular}{ll}
\hline
Paris & 21 degrees\\
Berlin & 19 degrees\\
\hline
\end{tabular}
\end{Table}
\begin{Table}
\caption{Another table}
\label{hightemperatures}
\begin{tabular}{ll}
\hline
Paris & 21 degrees\\
Berlin & 19 degrees\\
\hline
\end{tabular}
\end{Table}
% \begin{table}
% \caption{My table}\label{temperatures}
% \begin{center}
% \begin{tabular}{ll}
% \hline
% Paris & 21 degrees\\
% Berlin & 19 degrees\\
% \hline
% \end{tabular}
% \end{center}
% \end{table}
%
%
% \begin{tablebox}[title={My table}, label={temperatures},code={\par\medskip}]
% \tcbset{title=pft}%
% \begin{tabular}{ll}
% \hline
% Paris & 21 degrees\\
% Berlin & 19 degrees\\
% \hline
% \end{tabular}
% \end{tablebox}
%
\end{document}

So this works in principle. (Obviously I was not courageous enough to touch the table environment with a lower-case t, but in principle one could.) One could make \begin{center}...\end{center} work, too, by redefining \center and \endcenter, say, or putting the stuff in some appropriate box.
I did not do that for a reason: to show that there are things which work fine in one environment but less so in another. Trying to tackle all possible cases with LaTeX methods is very hard, or impossible, i.e. one will always find places where this breaks.
This is not to say that one cannot do a very good job at redefining these things. I just do not think one can do a perfect job. If you really want to go that way, here is a prototype that works in principle and shows one possible direction to go.