If you put the drive in a USB caddy you will see it as a regular external drive, it's just like plugging in a USB thumbdrive. You can then see the entire folder structure of that drive and as it was way before the time of user profiles, the folder structure is most likely pretty simple. Filenames were restricted to eight characters with an extension so it may take a while to figure out what everything is. I would simply start by copying the entire drive, every file and folder on it, to a single folder on your existing W10 system (retaining the folder structure of course) and do the searching in there. That way the Win3.1 drive will be unaffected and you can still go back and try to get it running on the old system. You can indeed use the regular search functions within Windows to find all doc files, or browse the folders to find a Psion one, things like that.
Edit: forgot to add that it's the first Windows 3.1 floppy that should be bootable. If you have a DOS 6.22 floppy, same thing applies.