If you're making a portable you probably need something to watch it on. (Unless you want to guess what's happening in the game, but I wouldn't advise that) Anyway, this forum is your "Hacking a pocket TV/screen" one-stop solution. Share your experiences and knowledge here.
an LDO regulator would do what you want (low drop out)
but it depends if you want to use one regulator, if you do you will need one that can output enough amps, id say 1.5 would definitly be safe
You can buy a 7805 at any electronics store (not LDO though) for (I don't know the exchange) less than 2 USD. If you want an LDO you either need a good electronics store, or to order from an online company.
Well seeing as it's free (and seeing as this computer has deepfreeze and I don't want to lose the product page ) I decided to order 3 of each of these:
I don't know about the SNES mini, but the PSone screen draws about 750mA un-modded, and about 350mA with the LED mod, so you may need to use 2 convertors anyways.
BTW, the DC-DCs that you're brother found have a 5V sister model, so those may be better, especially since they can handle up to 2A.