If I had time, I'd maybe tell the dude to wait outside, then get my loafers, walk with him to the shop and buy a meal. Strangers in my house? No thank you. Good way to get robbed in my neighborhood.
There are free showers and halfway houses around here, so getting shower wouldn't be a reason to knock on the door, I think.
Optimally, we should be housing everybody as its been proven time and time again how much cheaper it is than leaving people homeless. It's what I vote for every time, but somehow people are just too selfish.