Can I change the battery connector on this model aircraft safely?
The XT60 connector is rated for 65A continuous (per Sparkfun). JST is a manufacturer that makes lots of different connectors. In model aircraft and RC hobbies, I believe the JST SFH connector is quite common. This connector is only rated for 4A.

It sounds as though you have a small battery (assuming a single cell LiPo?) and a power management board that could potentially be used for much larger projects. In that case you should be OK replacing the XT60 with a smaller connector, as long as the project is never going to draw more than the connector's rated current.

If you later re-purpose the PMB for a different project, and it needs more current, don't use the under-rated connector!