The G602 takes AA sized batteries. The one you show I have no idea of the size but it's way bigger than AA.
Even if it did fit I wouldn't supply the mouse with a high current battery putting out 3.7v when the mouse would be looking for 3v max.
You're better off with these.
https://www.aliexpress.com/store/group/AA-14500-Battery/506629_511218316.html?origin=n&SortType=bestmatch_sort&g=y&PPValue=554-201447378