Had Grant been there the sentry would never have dared slip off for a drink or whatever it was. Booth would never have got in.
As to Wade, had Grant not been available they'd have nominated another well-known General - Sherman if he would accept it, or maybe Sheridan or Admiral Farragut. They wouldn't have gone for an accidental President of a few days standing.
Grant also had a competent bodyguard with
him who would not have left the Presidental
box to go off & watch the play as the jerk
who was assigned to Lincoln did(arrrrgh!)
Grant also said he would have heard Booth
coming in & stopped him; in fact for the rest
of his life Grant lamented that if he'd been
there Lincoln would not have been killed. I
tend to agree; & think Grant would also have
survived & Booth would have been captured.
Grant this would still have been alive in 1868
& thus, as IOTL, been elected President.