It's definitely worth checking with the company you bought the personal alarm from. I'd recommend sourcing one from them as it's not something you want to take chances with, you want the peace of mind that it will work properly.
Otherwise, you could buy an additional alarm so that your relative will have both a pendant and wrist alarm - although this is an expensive option.
No need to answer this if you don't want to, but have you fully considered the pros and cons for wrist alarm vs pendant? Is there a particular reason you want to switch? After caring for a family member who had a pendant alarm I do know a bit about them already but had a quick search for any related articles on the internet about it, this one might be useful if you're still stuck trying to decide:
https://www.helpline.co.uk/pendant-or-wrist-alarms/
Let us know if you had any luck!