I’ve got a SolarStorm2 and a replacement battery after the original suffered a total existence failure. However, the connection between the two isn’t perfect, so if I pull my wire it goes off.

Is there anything I can do other than remove the connector from the old battery and solder it on to the new one?

Squeeze the female connector with a pair of pliers to make it a bit oval and a slightly tighter fit. Could also try bending the pin just a touch if necessary. But – if the female connector is on the battery, ( (and I think they are) make sure you do the second step with a plastic tool.

If the above doesn’t work, you can always go with your first option.

No idea what your connections look like, but the male single pin can sometimes be a split type, which gets squashed whenever you plug or unplug. It can be opened up with a precision screwdriver. It’s a crap design because you have to re-do it whenever connection becomes poor. Have had this issue regularly with a nukeproof light (which was just an expensive Chinese generic job).