Noting
MrbmwX5's Key Fob DIY I grabbed the battery from Mouser, but instead of the vertical I grabbed BOTH Horizontal and Vertical because I read the issue with bending pins, snapping them off and reusing them, etc.... NO NEED, just get the vertical one instead.
The biggest difference of any value to you is that the pins are on the opposite sides facing opposite directions on the vertical whereas on the horizontal they are both facing the same way AND on the same side as well! (That's exactly what you want, see images below).
As you can see the vertical battery will need a good bit of work to fit, while the horizontal battery pins line right up and solder in with only a slight widening of their direction.
I recommend the horizontal pin version. In the end neither are perfect and both will work. This thread is just to show the differences in the two batteries so you can make your decision.