Muffling a fire alarm speaker?
No.    Your safety is worth more than you feeling anxiety.  You have smoke alarms for your apartment but this one looks like it is hooked up to the building.  Meaning if there were a fire somewhere else in the building you would be notified via this alarm.  

You may think that this alarm is extremely loud if you are standing next to it but what if you are in the shower with a radio on?  In college I had a similar alarm and showered right through a drill and had no idea.  Also these alarms should go off maybe a couple of times a year so your anxiety should be only messed with for a few minutes a year at most.

If this doesn't convince you, then maybe saying that tampering with fire alarms is illegal and could be grounds to have you evicted.