Having looked back at your first post now, can you see better how your issue with your mouth relates. Not only do you have the tension of your stroke arms but you have also built up tension from the arm using the stick…if that’s the hand you’re using it with. That’s one of numerous reasons why orthopaedics/physio’s like to avoid the use of walking aids as much as possible in general. But in particular with stroke survivors, because of the risks of teaching the brain bad habits, poor posture as it relearns muscle connectivity/reconnects in those areas affected.
Another thing you could try is regular neck and shoulder massage, either by a physio therapist/osteopath or even by just using an electric massager. If you use an electric one, I’d suggest you get your wife to do it as you probably won’t be able to do a thorough enough job of it.