However, thinking about it now, it would be inappropriate to keep a hold of them without the player's permission, regardless of my intent of killing them off swiftly. I think it would be easier if everyone ignored their character's involvement in the RP altogether, as if they were never there.
I think this is the best way to go about it In most RPs I've been in, this is ultimately the conclusion when someone does the disappearing trick, and I think it works very appropriately in this situation.
The best thing, at least, was that he gave the roleplay a tough time and you reacted immediately and efficiently. I just wasn't comfortable with the way you worded it; I thought, for some reason, Timberpaw's involvement, regardless of being a background character, would be prolonged within the RP, but I'm glad to hear you were planning to kill him off quickly. Ultimately, however, I'm glad you've deciding to go with ignoring; I think its the one that works best when RPs come to these bumps. I mean, sure, sometimes things might get rocky if those characters were in the middle of interacting with someone else...but at least you will have safely stayed within the rule of not touching somebody else's character without their permission, and then things move on and smooth themselves out!