Creating a macro that can selectively format capital letters

The tokcycle package (https://www.ctan.org/pkg/tokcycle) can be used for this.

\documentclass{article}
\usepackage{tokcycle}
\newcommand\famword[1]{%
  \resettokcycle%
  \Characterdirective{\ifcat A##1\ifnum`##1<`Z\addcytoks{%
    \textsc{\char\numexpr32+`##1\relax}}\else
    \addcytoks{##1}\fi\else\addcytoks{##1}\fi}%
  \tokcyclexpress{#1}%
  \the\cytoks%
}
\begin{document}
\famword{aKiLulat or even aK\textit{iLulat}!}
\end{document}

As I commented, to get italic small caps, you need a font that supports it, such as \usepackage{newtxtext}:

If one prefers an invocation that is more environment-based, rather than macro-based, there is this:

\documentclass{article}
\usepackage{tokcycle}
\tokcycleenvironment\famword%
  {\ifcat A##1\ifnum`##1<`Z\addcytoks{%
    \textsc{\char\numexpr32+`##1\relax}}\else
    \addcytoks{##1}\fi\else\addcytoks{##1}\fi}% <-CHARACTERS
  {\processtoks{##1}}% <-GROUPS
  {\addcytoks{##1}}% <-MACROS
  {\addcytoks{##1}}% <-SPACES
\begin{document}
\famword aKiLulat or even aK\textit{iLulat}!\endfamword
\end{document}

When using modern fonts in conjunction with LuaLaTeX or XeLaTeX, one is (sometimes) able to delegate this this to the font, since OpenType Layout defines a font feature c2sc that translates capital letters to small cap letters. Unfortunately, Latin Modern does not contain this feature. When available, one can activate this via fontspec feature Letters=UppercaseSmallCaps. Example:

\documentclass{article}
\usepackage{fontspec}
\setmainfont{Stix Two Text} % Font with c2sc feature and italic SC
\newcommand\famword[1]{{\addfontfeatures{Letters=UppercaseSmallCaps}#1}}

\begin{document}
\famword{aKiLulat}

\itshape \famword{aKiLulat}
\end{document}

Here's a LuaLaTeX-based solution. It consists of (a) a main Lua function called uc2sc (short for "uppercase to smallcaps", I suppose) and an auxiliary Lua function called makesc which, together, do most of the work and (b) a LaTeX macro called \famword that acts as a wrapper for the uc2sc function. The Lua functions employ Lua's versatile built-in string.gsub and string.lower functions.

% !TEX TS-program = lualatex
\documentclass{article}
\usepackage{luacode} % for "luacode" environment
\begin{luacode}

function makesc ( x )
   return ( "\\textsc{" .. x:lower() .. "}" )
end
function uc2sc ( s )
   return ( s:gsub ( "%u", makesc ) )
end

\end{luacode}
%% LaTeX wrapper macro:
\newcommand\famword[1]{\directlua{tex.sprint(uc2sc("#1"))}}

\usepackage{fontspec}
\setmainfont{Stix Two Text} % a font with italic-smallcap letters

\begin{document}
\famword{aKiLulat} 

\itshape \famword{aKiLulat}
\end{document}