Okay, so here's a solution. The goal is to use the answer from StackExchange to overwrite the footer definitions where the total number of slides is being added.
In RStudio, create a new "Text" file, copy the following into the file, and then save it in the same folder as your slides with the name header.tex.
\makeatletter
\setbeamertemplate{footline}{%
\leavevmode%
\hbox{%
\begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,center]{author in head/foot}%
\usebeamerfont{author in head/foot}\insertshortauthor\expandafter\beamer@ifempty\expandafter{\beamer@shortinstitute}{}{~~(\insertshortinstitute)}
\end{beamercolorbox}%
\begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,center]{title in head/foot}%
\usebeamerfont{title in head/foot}\insertshorttitle
\end{beamercolorbox}%
\begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,right]{date in head/foot}%
\usebeamerfont{date in head/foot}\insertshortdate{}\hspace*{2em}
%\insertframenumber{} / \inserttotalframenumber\hspace*{2ex} % old version
\insertframenumber{} \hspace*{2ex} % new version without total frames
\end{beamercolorbox}}%
\vskip0pt%
}
\makeatother
Then let rmarkdown know that this file needs to be added to the header of your slides by declaring it in the YAML.
---
title: "Untitled"
author: "Name"
date: "27/08/2019"
output:
beamer_presentation:
theme: CambridgeUS
includes:
in_header: header.tex
---
Now when you render (or knit) your slides again, only the slide number of the current slide will show!
Note that you can also use this opportunity to tweak the other elements that show up in the slide header and footers by poking around in the header.tex file.
