I wouldn't want to give Wilson the keys. For one, I don't think he has the same football savvy as guys like Tom Brady do. Guys like Brady and Manning made a living at the LOS, dictating the game pre-snap. They acted as the defacto offensive coordinators later in their career. I haven't seen Wilson demonstrating that ability yet. Often times his last minute changes at the LOS are suspect. He has been defined by his ability to go off script and improvise. I wouldn't call him a field general yet. To be fair, a lot of that are probably limits put on Wilson by Pete Carroll. That being said, he just hasn't shown me enough to say "yes you can be player and coach at the same time."
Even for guys like Manning and Brady, could run a team in addition to fulfill their player duties. It's just too much to take on. Scouting, defensive/offensive game planning, player grievances, staff hiring, general management of underling coaches, etc is enough on its own. Wilson also hasn't really been brought up in a modern NFL offense either. I don't think he'd have a grounded philosophy to build on and he has no previous NFL coaching experience.
If Pete were fired tomorrow I'd just assume hand the keys to Shane Waldron for the rest of the year, fire KNJ, promote a assistant/positional coach. Have Wilson and Shane split some of the duties on offense.