The HRM chest straps I typically use are not ANT+, they are an older electronic standard than that. Takes a large coin in a slot in the round battery cover to turn it.
I have a Garmin ANT+ strap, a cheaper version, that also has a round cover that uses a coin in a slot. I looked on Ebay for a photo of a Garmin like mine, this one looks like it.
https://www.ebay.com/itm/Garmin-HRM1...P/264883811312
In one of the photos it shows the back side of it, there is a round battery cover, a coin fits in that slot to turn it.
I am not recommending that particular Ebay listing, I only looked at it for a listing that has a photo to refer to.
I often replace my own watch batteries. I find it is easier to get the screws out if I put some grease on the screw threads before I screw them in. So, if you can ever get the screws out, you might try grease on the threads before you re-assemble.