I just replaced the battery of my polar rs300x last week.
You can easily get the battery in Migros, Coop or any place that they sell battery. In my case, it was the "CR 2032", quite common battery (around 2CHF?).
I can imagine that most of the watches, the process will be as simple as with the RS300x. Usually as soon as you unscrew the screws from the back, you will see the battery right away.
There is one potential problem though: water resistant seal!!!!! I can imagine that if you send it to Polar, they will make sure that the watch is properly sealed (against water). Or at least, it will be done by people with more practice, so it is more likely that they will put the lit back in its proper place. In fact, I think this only depends on how 'handy' and careful you are, and that is not rocket science, just taking care and taking the risk.
In my case, I saw a thin piece of rubber that sealed the watch, and that was all. I am not sure if it's 100% sealed, but I think is worth the risk
If you take it to some watch shop in Switzerland, they for sure will have more practice doing this operation and it takes 5 mins. There is nothing special with being Polar or being a HR. So you could consider taking to a shop as well.