Help with better isomorphic function symbol

Question

I'm trying to us TikZcd to create a better isomorphic mapping symbol. I've seen the other posts about this issue and they're all terrible, and they even acknowledge their solutions aren't great. The symbol for a map which is an isomorphism?

I personally think the arrow below is kind of nice (with some adjustments), where the example is the arrow from 1 to 2:

This is produced by the code

$1 \hspace{-0.4cm} 
\begin{tikzcd}
  \phantom{1} \arrow[r, "\sim"] & \phantom{1}
\end{tikzcd} 
\hspace{-0.4cm}
2$

Since, this is a bit messy, I wanted to put this into a command like so

\newcommand*\isomap{
\hspace{-0.4cm} 
\begin{tikzcd}
  \phantom{1} \arrow[r, "\sim"] & \phantom{1}
\end{tikzcd} 
\hspace{-0.4cm}
}

But I get the error

Package pgf: Single ampersand used with wrong catcode.

I've looked up this error but the results aren't relevant to my situation (as far as I can tell). Any ideas on how I can get this into a command?

Answer 1

Another suggestion, with stackengine:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}%
\usepackage{old-arrows}
\usepackage[usestackEOL]{stackengine}
\newcommand{\isomarrow}{\mathrel{\setstackgap{S}{-0.5pt}\ensurestackMath{\Shortstack{\scriptstyle\sim\\ \longrightarrow}}}}

\begin{document}

\[ 1 \isomarrow 2\]%

 \end{document} 

Answer 2

A possible solution without tikz-cd, using \xrightarrow with a box in predefined length (I used 1cm).

The command contains 2 arguments to be used as domain and codomain, like \isomap{x}{y} for example.

\documentclass[11pt,a4paper]{report}
\usepackage{amsthm,amsmath,amssymb,amsfonts}

\newcommand{\isomap}[2]{$ #1 \xrightarrow{\makebox[1cm]{$\sim$}} #2 $}

\begin{document}
the operator $\otimes$ is invariant up to isomorphism \isomap{1}{2}.

the operator $\otimes$ is invariant up to isomorphism \isomap{x}{y}.    
\end{document}