Besides law enforcement, every bounty hunter in the land would have been hunting for him. His “Dead or Alive” wanted poster would have had a huge number on it, and the penalty for harboring or aiding him in any way would have been very severe.
The person who received a severe sentence for aiding Booth was Samuel Mudd. He escaped the death penalty by just one vote. His descendants have argued that he was just a country doctor helping an injured stranger; they and others have pushed for his conviction to be expunged. However, evidence shows that he had met Booth at least twice, possibly to discuss a plot to kidnap Lincoln.
The obvious solution here is to shave beforehand, then don a fake moustache.
I’ve read some of the documentation recently, that certainly disputes the general idea that Dr. Mudd had no idea who he was treating. As I recall, Roger Mudd, longtime American television newsreader was a distant relative.