I know this is an old post, but just commenting here in case it's still useful.
I reached out to Schaffner in regard to this about 2 years ago. They (very helpfully) tracked down an employee that had been there well over 2 decades. He said "I do believe Schaffner was using paper caps back in the 80's. Maybe early 90's. But film caps are the norm now, except for small value Y caps (nF, pF) that are ceramic." From that, I'd say your 3458A is probably safe. However, if you are thinking of replacing it to be extra sure, I've done it and it's not too difficult. You can drill out the rivets (center punch them first). I then used a pair of metal snips to finish the job.
Keysight now uses Schaffner FN9222-3-06 for this, so that's what I replaced it with. I used a flathead M3-10mm screw, a lock washer, and nut. There was no damage to the instrument in the process and the replacement looks like it belongs perfectly. I've used this instrument quite a bit since then and it works perfectly.