The existing battery is an LTC-7P that was hard to get hold of, there are still some stocks circulating but they are either expensive or not able to deliver outside the US. 

So  I had to look for a replacement, there is an equivalent from EVE with the same form-factor the EF651625 but tbh I didn't know the brand and couldn't find any reviews on the internet so I opted for a SAFT LS14250CNA. It has slightly more capacity but got a cylindrical shape, this particular one fits and th pinout kind of workout since the board only needs 2 connection rather  than the 4 on the previous battery.

#1: install a backup battery or any stable 3.6V source, these can be soldered on the pins of the diode and resistor just below BT2570. If voltage on this rail is lost during the operation the calibration data will be gone. 
Now, I've read somewhere that recalibrating the scope is not as expensive or as difficult as people think, well! it will be always more difficult and more expensive than keeping poer during the swap.

#2: remove battery, as you can see the negative pins are connected together so a 2 pin axial battery would work perfectly as long as the pitch is smaller than 35 mm and the diameter is around 15mm. if it gets bigger than that there is risk of touching the casing.  

#3: New battery soldered and backup removed

Note: the dodgy tape was just to avoid shorts