You can do whatever you and the tenant agree to do.
I do not allow tenants to remain without a lease. I send to them a notice (certified mail) which simply states that if they choose not to sign the new lease, they are required to move by _____date. It is their notice of termination. If they remain past that date they will be evicted.
I cannot see why it would be time consuming to have him leave. I have sent the 'consequences of eviction' letter to tenants to warn them that staying past the termination date will result in eviction and all the bad repercussions on their future ability to rent anywhere decent. eviction for hold-over is fast and easy. you don't even have to post a 'cure or quit'..just go file.