I can sympathize. We had a chocolate lab who was scared of the low battery warning beep made by a smoke detector, of which we have several at home. Not an everyday problem like a microwave but still...
There are multiple brands of microwaves in Airstream trailers. It might help to list the brand that you have. We have a Contoure in our 2020 Globetrotter and there is nothing in the manual about disabling the beep. Maybe a call to the manufacturer of yours would yield a result.
2020 25' Globetrotter Twin | 2017 F250 4x4 6.7 max tow Platinum
400Ah Battle Born lithium battery string | 580W solar (400W roof 180W portable)