A snap cap is a specially designed inert round. Depending on quality, it is usually constructed of aluminum or plastic, and incorporates a small area around the "primer" to cushion the impact of your firing pin.
Dillon Precision sells aluminum (A-Zoom) snap caps. You can also find Pachmayr plastic snap caps, which incorporate a spring-loaded cushioning system for the "primer" area. The cheapest are the Saf T orange plastic snap caps, which are just plastic shells without any special features.
I don't know about the Remington 870 (I tend not to go through my dad's stuff any more since he discovered I had copied the keys for his Porsche back in high school
) but I'd bet that 870s have a firing pin spring.
In such an instance, dry-firing will not hurt your gun but it never hurts to have snap caps for practice. My Benelli M1S90 has a firing pin spring so I use the Saf T snap caps, mostly for practice of reloading and switch-to-slug drills.
Yes you can use an inert hull if you resize the hull back down to factory spec -- I'm sure you can do that with a shotshell press, although I don't know first-hand since I only reload metallic cartridges. Since the primer has already been fired, a home-made dummy will not have the cushioning effect on the firing pin, unless you replace the dead primer with an eraser from a pencil or something similar.
Be forewarned that it can be easy to mix up "dummy" rounds made at home on the reloading press and live rounds. For that reason, I use the orange Saf T snap caps, because then I know I can't get my snap caps mixed up with my live rounds.
HTH,
Justin
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Justin T. Huang, Esq.
late of Kennett Square, Pennsylvania