Just did some reading and unfortunately you won’t be able to use the smart ring with the yale doorman.
The ring contains a t5577 (lf or 125khz) emulator chip and a ntag213. This ring is almost identical to the NExT implant. The yale doorman on the other hand requires a mifare classic emulator in implant terms xM1 or flexM1 and others.
Check out this thread for useful information:
If your set on a ring take a look here (first link i found no affiliation)