Why would Tyrion surrender? Stannis would kill Joffery and Tommen, likely Cersei, and the rest of the Kingsguard and any loyal to those three. There is no chance his father (the most dangerous man in Westeros) sees him as anything but traitor, and even Jamie wouldn’t look at him fondly anymore. His only hope would be to betray his family in whole and take service with Stannis, and that’s a very shaky bit of ground there. Stannis might just hold him hostage (or kill him) for Tywin’s crimes.