\TeX in small caps?

Somehow this is a non-answer, but I'd suggest to stick with \textsc{\TeX shop}. What is the idea of small caps, after all? They use the usual capital letter, and only for small letters it's "small capital letters", in short "small caps". And the letters in \TeX are all capital from the start, so nothing should change there.

If you really want everything in small caps, then you easily find the definition of \TeX by \show\TeX; the result is essentially shown in Pieter's comment to the question. Some fiddling with the spacing yielded

\documentclass{minimal}
\begin{document}
\textsc{t\kern -.12em\lower.4ex\hbox{e}\kern-.1em xshop}
\end{document}

Seamus,

I thought this was an interesting (and surprisingly challenging) question, and I'm not sure what the best solution is, but I went ahead and created a few macros for various options, just to see what various possibilities might look like.

Independent of whatever solution is used, one thing I would recommend is to insert a very tiny amount of horizontal space after the \TeX, just to ensure that the X doesn't run into the S visually. A hair-space is too wide, but \hspace{.03em} seems to do the trick.

Here is what I came up with. First a picture:

My favorite for regular use is (1), and for small-caps use my favorite is (2a)—although (3b) doesn't look too bad to me as long as there is a slight amount of space between the X and the S.

And now the LaTeX code. I started with Hendrik's kerning of \TeX in small caps, wrapped it into a \scTeX control sequence, and built up options from there:

\documentclass{article}
\usepackage{booktabs}
\begin{document}
\setlength{\parindent}{0in}

% \TeX in small caps
\newcommand\scTeX{%
  \textsc{t\kern -.12em\lower.4ex\hbox{e}\kern-.1em x}%
}

% 1. TeXShop natural with \TeX with regular "Shop"
\newcommand\TeXShop{%
  \hbox{\TeX\hspace{.03em}Shop}%
}

% 2a. TeXShop with uppercase \TeX with small caps "Shop"
\newcommand\TeXscShop{%
  \hbox{\TeX\hspace{.03em}\textsc{Shop}}%
}

% 2b. TeXShop with uppercase \TeX with small caps "shop"
\newcommand\TeXscshop{%
  \hbox{\TeX\hspace{.03em}\textsc{shop}}%
}

% 3a. TeXShop with small caps \TeX with small caps "Shop"
\newcommand\scTeXscShop{%
  \hbox{\scTeX\hspace{.03em}\textsc{Shop}}%
}

% 3b. TeXShop with small caps \TeX with small caps "shop"
\newcommand\scTeXscshop{%
  \hbox{\scTeX\hspace{.03em}\textsc{shop}}%
}

\begin{tabular}{lll}
\toprule
%\multicolumn{2}{c}{Item} \\
%\cmidrule(r){1-2}
%& Appearance & Description \\
%\midrule
(0) & TeXShop & unadorned\\[2pt]
(1) & \TeXShop & natural\\[8pt]
(2a) & \TeXscShop & regular ``\TeX'' with small caps ``Shop''\\[2pt]
(2b) & \TeXscshop & regular ``\TeX'' with small caps ``shop''\\[8pt]
(3a) & \scTeXscShop & small caps ``\TeX'' with small caps ``Shop''\\[2pt]
(3b) & \scTeXscshop & small caps ``\TeX'' with small caps ``shop''\\[2pt]
\bottomrule
\end{tabular}

\end{document}

Note: this code only works for regular 10pt roman text. It fails quite poorly for italics, slant, and boldface.

What did you end up doing for a small-caps version of \LaTeX?