Making pause in a diagram

I would use overlay-beamer-styles for that.

\documentclass{beamer}
\usepackage{tikz-cd}
\usetikzlibrary{overlay-beamer-styles}
\begin{document}
\begin{frame}[t,fragile]
\frametitle{A commutative diagram}
\[\begin{tikzcd}[sep=huge]
 \mathcal{H} \arrow[d,"?"{swap,visible on=<1>},"W_A" {swap,visible on=<2>}] 
 \arrow[r,"T"]& \mathcal{H} \arrow[d,"?"{visible on=<1>},"W_A" {visible on=<2>}]  \\
\mathbf{R}(A^{1/2}) \arrow[r,"\widetilde{T}" swap] & \mathbf{R}(A^{1/2})
\end{tikzcd}\]
\end{frame}
\end{document}

The overlay-beamer-styles library has several advantages, one of them being that it avoids jumps. To see this consider an example with \only:

\documentclass{beamer}
\usepackage{tikz-cd}
\begin{document}
\begin{frame}[t,fragile]
\frametitle{A commutative diagram}
\[\begin{tikzcd}[sep=huge]
 \mathcal{H} \arrow[d,"W_A" swap] 
 \only<1>{\arrow[r]}
 \only<2->{\arrow[r,"T"]}& \mathcal{H}
 \arrow[d,"W_A"]  \\
\mathbf{R}(A^{1/2}) \arrow[r,"\widetilde{T}" swap] & \mathbf{R}(A^{1/2})
\end{tikzcd}\]
\end{frame}
\end{document}

On the other hand, the analogous construction with overlay-beamer-styles does not jump.

\documentclass{beamer}
\usepackage{tikz-cd}
\usetikzlibrary{overlay-beamer-styles}
\begin{document}
\begin{frame}[t,fragile]
\frametitle{A commutative diagram}
\[\begin{tikzcd}[sep=huge]
 \mathcal{H} \arrow[d,"W_A" swap] 
 \arrow[r,"T" {visible on=<2->}]& \mathcal{H}
 \arrow[d,"W_A"]  \\
\mathbf{R}(A^{1/2}) \arrow[r,"\widetilde{T}" swap] & \mathbf{R}(A^{1/2})
\end{tikzcd}\]
\end{frame}
\end{document}

It it true that in the special case of your example this is not an issue, but in general it is.

Here is a solution for the left one. It can be done in the same way for the right one.

\documentclass{beamer}
\usepackage{tikz-cd}

\begin{document}
\begin{frame}[fragile]{frametitle}{subtitle}%
\[
\begin{tikzcd}%[sep=huge]
 \mathcal{H} \only<1>{\arrow[d,"?" swap]}\only<2->{\arrow[d,"W_A" swap]} \arrow[r,"T"]& \mathcal{H} 
 \arrow[d,"W_A"] \\
\mathbf{R}(A^{1/2}) \arrow[r,"\widetilde{T}"] & \mathbf{R}(A^{1/2})
\end{tikzcd}
\]
\end{frame}
\end{document}