I don't use a headset for calls (not often; last time I used it, it was plugged into my MacBook Pro to do a FaceTime audio call), but since nobody else is answering yet...
Try these ideas (just spitballing here) --
- Initiate the call from the headset. Do a "Hey Siri, call so-and-so", or "Hey Siri, call 345-555-4242" using the headset mic, or however it operates.
- If the headset is bluetooth, pair it with the watch instead of the phone. You'll probably have to unpair it from the phone first, then pair it with the watch, otherwise it might get confused (or so I've read; I haven't tried a bluetooth earpiece in at least six or seven years).
That's all I've got. What else have you tried?