No, because I've noticed that once you get the Triforce, if Ganon is in another room, he'll never appear there...
Defeat Ganon, get item other than Triforce
Why not create a custom boss? It might be a little difficult (I haven't tried this yet myself) but in idontknow's tutorial (http://www.geocities.com/idontknowtutorial/contents.html?1048292445858) he tells you how to create a custom boss. You could make something that looks/acts like Ganon (maybe even be a weaker version so that when you get to the final dungeon, he's also gotten stronger) and then you can set his as a normal dungeon boss.
It'll look like Ganon, act like Ganon, but won't be the actual Ganon sprite from the game (You could copy/paste the graphic) and then you'd be able to set whatever item you wanted, just like with a regular Dungeon Boss. Would that work?
I know that it is possible to get another item other than the triforce, but I don't know how. Want proof? Well, in Isle of the Winds, I recall having to fight a fake Ganon and wait... crap, I don't remember if he dropped a triforce or not. I suppose there is a theory that I haven't tried yet - Enter the room and make sure you appear on a floor of Layer 1 and then when the triforce comes in it would be on layer 0. Just note that I am a newb to layers and honestly don't really get how they really work, so that might be incorrect (I'm getting to layers later, as I will probably need 'em in dungeons, hehehe). Anyways, can't you just play the game with the triforce anyways? But yeah, I would REALLY like to be able to fight ganon multiple times as I have planned that in my quest, hehehehehehehehe............. no you won't have to fight him until the last level there. And don't expect my quest to be out for a while. Heck, a demo would take a little while. Aside from all of that, I'll repeat it - it currently IS possible to not pick up the triforce from him.