Sample scenario:

One service desk have 20 request types.
10 of them are assigned to specialist A
5 to specialist to specialist B
5 to specialist to specialist C
So button will be not enough as there are different specialists for different tasks and there is no a default specialist.
I suggest to add smth like 'Technician Availability Chart' or calendar.
If a specialist is not available on a specific date range - you can mark it in calendar. As an option - you can choose a Backup Technician rule for this period.

• Move requests to unassigned state.
• Assign to following technician
• Don't take any action on the requests.

Also it would be nice to see in this calendar all technician's requests and reassign them from current technician to another specialist if needed.