What gauge wire do I need to connect a 3.7V 750 mAh LiPo battery?
The conductor thickness needs to be chosen relative to the current flow ie a higher current needs thicker conductors and as voltage increases the insulation tends to be thicker / better.

However, the voltage drop or losses also mean that a thicker conductor can be necessary.

You need to specify the maximum current to flow then as suitable size can be selected.