Customize `\citeauthor*` to show full author name but UpperCase only the first letter

We can very easily define a new command \citeauthornsc and \citeauthornsc* from the standard definitions of \citeauthor that does not print last names in small caps by adding \renewcommand*{\mkbibnamefamily}[1]{####1}% to the pre-code hook (the vast number of #s is necessary due to the way commands are redefined within commands); the pre-code hook has only local scope, so that the redefinition applies only to this cite command. The two commands are basically a copy of biblatex.def's definitions with that one line added to the precode.

\documentclass{article}
\usepackage[french]{babel}
\usepackage{csquotes}
\usepackage[backend=biber,style=verbose-trad1]{biblatex}

\addbibresource{biblatex-examples.bib}

\DeclareCiteCommand{\citeauthornsc}
  {\renewcommand*{\mkbibnamefamily}[1]{####1}%
   \boolfalse{citetracker}%
   \boolfalse{pagetracker}%
   \usebibmacro{prenote}}
  {\ifciteindex
     {\indexnames{labelname}}
     {}%
   \printnames{labelname}}
  {\multicitedelim}
  {\usebibmacro{postnote}}

\DeclareCiteCommand*{\citeauthornsc}
  {\renewcommand*{\mkbibnamefamily}[1]{####1}%
   \boolfalse{citetracker}%
   \boolfalse{pagetracker}%
   \usebibmacro{prenote}}
  {\ifciteindex
     {\indexnames{labelname}}
     {}%
   \printnames[][1-1]{labelname}}
  {\multicitedelim}
  {\usebibmacro{postnote}}


\begin{document}
Standard small caps:
\citeauthor{wilde}
our new command:
\citeauthornsc{wilde}
small caps again:
\citeauthor{wilde}
\autocite{wilde}
\end{document}

As of March 2016 (biblatex 3.3), you need to change

\mkbibnamefamily

instead of

\mkbibnamelast