I am a pretty overprotective ferret owner. I try my best to give my ferret play time every day like he needs. When I go on trips for a few days, I have a friend of mine go to my house to feed and water the pets and take care of them. The issue is that none of them have the time to sit and play with him or let him roam. Will my ferret be okay for a few days stuck in his cage until we get back?

I don't have time for my 3 to all get out for 4 hours and play but have found that a few 15-20 minutes at a time works great for us! Not sure if your friends or family have the time to make a couple trips over there to do that but it could be a suggestion :) 

My only two friends that are trust worthy enough to take care of my pets are both fairly busy. And one of them is simply not fond of my ferret to boot.

:( who doesn't like them!! They are adorable!!! :) I understand time restraints... I think if they have plenty of food and water they should be fine for a few days. Or if you have a bathroom or spare room you could ferret proof while gone you could leave them shut in the room

I only have one ferret and I just don't want him to get depressed or something because he's stuck.

few days no big deal. If he has lots of toys they could try to swap them when they go over to feed. Also just letting him out while they do food, water and litter will at least get out some energy. 
We have the ferret playpen and when we go out of town and don't take em with us we have our sitter let them loose in the pen when she is there. If you travel often you may want to invest in that so while they are attending to the cage the ferrets can run around without your sitter having to keep a close eye on them 

I've left mine for a weekend before (Friday afternoon to Sunday night). That's three of them though, they were okay but SUPER hype when we got home. I'd imagine a few days would be fine. But even if your friend only has 20 minutes to play with him it is better than nothing. 

Should not encourage the friend who doesn't like the ferret to play with it... animals seem to know and people who are more weary of an animal are more prone to mistakes.