Depends on the design of the novelty cap. For instance, your Vault 13 cap is perfect for SA profile, very happy that it tipped, by the way
Suits the Nuclear Data Green set, too. I think it's a good idea to match to Group Buy sets or sets with similar colours.
It also depends on who makes the cap. SP cannot do Cherry profile, but DCS is close enough for the row that most use for putting their novelty caps on (F key row on TKL and numbers row on 60%).
DCS is quite a bit lower profile than OEM (which stands for Original Equipment Manufacturer), although there are actually a number of versions of OEM, since each keyboard manufacturer can make their own keycaps and they don't end up exactly the same. So even if you choose OEM profile, they won't match the keys on all "OEM" keycap sets. Then again, OEM is still the most commonly used profile, since many people just keep using the stock caps that come with their board.
So for a "generic" novelty cap, OEM profile dyesub can work, but most people just go SP DCS Row 1.