Don't worry, even though he's still very much busy blushing, Inigo will grab that hand that's being extended towards him all the same for a handshake. (Even though he's a little unsure why the idea of all this is so surprising to Dennis - it's a pretty equal exchange, right?)

"Alright then."

He nods, before finally letting go of the hand again.

"It might have to start after today though. For today I'm rather.."

Um. How to put this in a way that means he won't have to explain his actual problem.

".. busy." Nailed it. "But perhaps tomorrow?"