Hi @viljokippel
Here's the ifixit [guide|167461] guide that shows how to replace the battery.
The battery model number is [https://www.google.com/search?client=firefox-b-d&q=361-00086-23+suppliers+canada|361-00086-23] (supplier examples only)
Search online for the ''part number only'' to find suppliers that suit you best.
If you don't want to do the repair yourself, then it may be best if you get a replacement battery first and then take the watch and the battery to a reputable, professional mobile phone repair service and ask for a quote. Also copy the link to the repair guide above and take that as well. Doing this should minimize the time required for the repair and therefore the cost