What will going happen if David "Big Papi" Ortiz sign to any different MLB teams?

Lets be real he's old and on the decline. He also is not a Hall of famer which could give him a little pull in the free agent market. If he signs any deal longer than 2 years, 3 at the most I would be astonished. The only reason for boston to keep him around is his leadership. He might make some noise offensively this year but i doubt it and i don't think many teams want to take a chance on him. Especially since he will only be DHing which eliminates 15 team right off the bat.

Possible Teams- White Sox- They loving picking up washed up power bats ( Canseco, Thome, Dunn)
Tampa Bay- Papi will be cheap which makes the rays a suiter. He will be back with Damon as well and be able to compete against the Sox