You have to define new symbol fonts; the relevant declarations are
\DeclareSymbolFont{mdputsymbols}{OMS}{mdput}{m}{n}
\DeclareSymbolFont{mdputlargesymbols}{OMX}{mdput}{m}{n}
\DeclareMathRadical{\sqrtsign}{mdputsymbols}{"70}{mdputlargesymbols}{"70}
Here's an example; the two \let
instructions are to keep the old symbol for doing a comparison. In the output, the new one (Utopia based) is on the left.
\documentclass{article}
\let\oldsqrtsign\sqrtsign
\DeclareSymbolFont{mdputsymbols}{OMS}{mdput}{m}{n}
\DeclareSymbolFont{mdputlargesymbols}{normal}{OMX}{mdput}{m}{n}
\DeclareMathRadical{\sqrtsign}{mdputsymbols}{"70}{mdputlargesymbols}{"70}
\begin{document}
$\sqrt{abc}$
{\let\sqrtsign\oldsqrtsign$\sqrt{abc}$}
\end{document}

Notice that this uses up two font alphabets (there are only 16 available), just for that symbol. It's not avoidable, as radicals need to be taken from a math font.