What I did was use a full team of 6 from my game, directly from the cartridge. You don't have to use the Yellow Version Pikachu; any will do (I got Surf on my Yellow Pikachu first, then got it on a couple of Red Pikachus). I don't recall whether you can use some rentals or not, but I would avoid doing so to be safe. Definitely don't use a registered team. Pikachu definitely needs to be in the team of 3 for the final battle; I don't recall if if needs to be in the team of 3 for the others or not.
The trick is that you don't actually need a full team of Pokemon to beat the Prime Cup R2. Mewtwo + one or two others should be sufficient, because Amnesia Mewtwo is super overpowered. Training it from level 70 to 100 via the Dodrio GB tower isn't nearly as bad as it sounds, and if you're willing to duplicate Rare Candies (and perhaps vitamins) with the Missingno glitch, it makes it that much easier. What I did was used my Red team (because my Yellow Pikachu was only in the mid 20s level-wise at the time), and trained Mewtwo, Blastoise (my starter), and one or two others to level 100 (without glitches). (I dragged along a spare junk mon or two to fill my Hall of Fame, but never brought those into battle.) Each battle consisted of sending out Amnesia Mewtwo, switching to Blastoise, Charizard, or Zapdos if things became dire for some reason or if I thought my opponent was going to put my Mewtwo to sleep or freeze it, and sweeping my opponent. I think I only lost a Pokemon in one of the battles, so it worked pretty well.