Search & Replace with different text style?

I’ve been told that to get permission to use a trademark, I must search & replace the uses of the trademark to change it to small caps or italics.

Is there a way to do this in Scrivener, or am I stuck going through my entire manuscript and changing each instance manually?

There’s no way to do this within Scrivener, but you may be safer doing it post-compile anyhow to ensure you’re getting the proper small caps style in the final version. Small caps are a particular variant that not all fonts have, so you may need to use a separate font for the trademark text. Word or OpenOffice or the like will have the tools to do a find/replace on the style like this to change the font, size, etc. as needed.