This is a sticky wicket. If you do not have the temperament or space to put someone up, then it might be better to not do so, rather than embarrass them or make them feel unwelcome.
We had a situation where a presumed Meshulach (a total stranger) came by our house and knocked on the door late at night wanting to sleep over. My husband asked him to wait a moment outside, gave him a drink and came to me in our room to tell me that he wanted to allow him to sleep over (hubby’s middle name is Avraham, and I think he takes that seriously).
We had three teenage daughters at home at the time, and I told my husband that due to my discomfort with this, we were not taking in a complete stranger late at night, especially when the whole situation seemed a little sketchy to me. BUT, on the chance that he was really just a simple meshulach who didn’t realize how late it was and missed his ride back to Williamsburg, I told my husband I was totally on board with paying for him for a night in a motel, and we would drive him there. He did not hear our exchange at all (both of my not wanting him to stay or of the offer to pay for a night’s lodging) and when my husband went out to tell him our decision (a process which took less than two minutes), he had disappeared.