Let me outline your thought process for sixty seconds so that this would be easy to explain to management.
1. If you push the silent alarm what happens? Police immediately believe you have a robbery situation. This means they are in route speeding toward your bank; this could cause someone to get killed in a car accident. It will also take several minutes for the response as the call center contacts your bank to see if you have a robbery situation.
2. If they call the police or have someone else do it they still have to leave the teller line to talk to someone in the back office or manager's office depending on your floor plan. The check passer will hear them talking on the telephone if conducted at the teller line.
Now that leaves us with a question how do the police want to respond to this situation? Contact the detective who is handling the case. Does he/she want a direct call or a telephone call to 911? The detective most likely will want you to call the dispatcher directly so he/she would provide you a direct telephone number to it.
Once you know how to call we would want to keep our staff safe. So I would have the teller state something like, "Oh I have to ask about this type of check as I am new." Or the teller could state, "I need to get approval for this check." The teller should turn and walk away to the rear area to call the police at their desired number. If the presenter of the check starts to state that it is OK or "I can take the check back," have the teller keep walking unless threatened.
Normally the presenter will be sprinting to leave the building when the teller goes to the rear area. If the presenter doesn't they will be there to discuss with the police how they came into possession of the check. The main thing here to keep everyone safe— staff, public and vendors. If the presenter threatens anyone or shows a weapon, have staff respond to it like a normal bank robbery.