If I disconnect the hoses used for the tilt function on the loader bucket and use them for the angle function on a snow plow can it harm the tractor hydraulics?
Not knowing your skills, anything is possible...

but at a high level, it should not cause damage to the tractor.
So without the curl/dump how are you going to keep the plow level with the driveway/road surface?
Cant afford a 3rd function remote right now, or damages to the tractor.......
This reads like.... I know what the right way to do this is, but I'm choosing not to do it, and am going to jerry-rig something together, but I can't afford to fix it if I screw something up.
That should be warning enough not to do what ever your attempting. If, and admittedly its a small if, something goes badly, then you've likely disabled your tractor until you save enough to make the repair.
While not idea to plow/clear snow with a bucket alone, it is an option. The other thing to consider might be a low cost rear blade. Usually the local want-adds have them for reasonable price, or you can get a light-duty one from the local farm/implement store.