Weapon, you seem to be a little confused... you can't stay in the game and just insert the next disc since opening the lid to do so bumps the Saturn back to the BIOS screen. ;-) That's why you save your game, then *boot* with disc 2 (and reload your saved game from there). So you do the swap trick with discs 2, 3 and 4 the same way you did with disc 1. Simple...
And no, with a mod chip you won't have any problems of any kind...