Theres two ways you could get around things:
As long as the rest of the logic board is good you could just get a replacement battery and plug it in by passing your systems battery by just unplugging yours and plugging in temporally the replacement (returning it paying the restocking fee). But that assumes the logic board is still working enough to get your data.
The second way is getting a OWC case which is designed to hold your Apple SSD. Then you have everything available! And you have a spare drive as well. This in my mind is the easiest way! [https://eshop.macsales.com/item/OWC/MAU3ENPRPCI/|OWC Envoy Pro]
As far as getting a bench power supply other than hooking it up at the MagSafe port it can get complicated depending on what happened with the charging logic and/or power rails.
Frankly, there are people who have the skills to fix your logic board! If your system is still in good shape mechanically then it might be worth fixing.