After editing the code, you have to bump the version number, then select the extension and use the Check for Updates button. It should realize the extension has changed and let you install the updated one, then all you have to do is restart PSM.
BTW, even if you don't bump the version number, you can uninstall the old extension and install the new one without exiting PSM, then just restart PSM for the changes to take effect.
No, there is no way to update the extension without restarting PSM at least once.