Since this is a Savage Worlds question, it seems best to take into account what the book has to say (from the GM section on Extras):
Though it’s rarely written, most games assume that the Game Master
controls the nonplayer characters, both when they’re being talked to
and when they fight alongside the player characters in combat. Most of
the time, this means the overworked GM simply forgets about the
additional characters during a fight, or shoves them off to the side
and narratively describes what happens to them. This goes for
hirelings as well as animal companions, sidekicks, or love interests.
The simple fact is that in most games, allies are a cumbersome
Savage Worlds takes a very different approach—we turn
control of allies over to the player characters. The GM acts out these
allies when they’re spoken to, of course, but he should very rarely,
if ever, take them over in combat.
...This can take a little getting used to. If you’ve been Game Mastering other games for a long time and have a hard time letting go of the nonplayer characters, we suggest you try it for a bit and see how it works out. You can always change it if it doesn’t make sense for your group.
Having run Savage Worlds a great deal, I would agree with this advice. It's much easier for the GM to let the players take control of the allies (which naturally means giving them the stats) and players enjoy getting to run other characters.
Your first concern about doing this was that allies might just be a big stat block rather than a character. I'm not sure what your players are like, but I would hope that they would be just as capable as you at providing them with a personality. You are able to when you have the statblock, so why can't they? Also, I strongly encourage rolling on the Ally Personality table (Chapter 4: Situational Rules under the "Allies" section), which goes a surprisingly long way towards breathing life and character into extras. Including roleplaying Hindrances as well can help a lot.
As for your second concern about the inability to fudge rolls, I think that this might be a sign of a deeper problem. After all, you can't fudge player rolls and I presume your game goes okay, so why would you need to fudge ally rolls? Is the encounter too difficult for the number of characters? Do you feel that you can't accept the possibility of failure or ally death?
That said, one trick I use in Savage Worlds when I really want to fudge player dice is that I reveal the penalty or bonuses to the roll after they roll (or I just make them up after the roll). The characters succeeded a bit too easily at the heal check? Turns out there was poison in his system that added a –2 penalty. Or if they just barely made it, there wasn't. You can try this with bonuses as well, but I think that this is harder to pull off as it can lead to the feeling that players will succeed no matter what. If you go this route, use it sparingly!
At the end of the day, I'd say that you should follow the Savage Worlds book's advice and always hand over the allies. As it says, "try it for a bit and see how it works out. You can always change it if it doesn’t make sense for your group."