I have an APC UPS at the S&B to keep my internet connection alive. Was not all that expensive. I don't recall exactly what model it is as am not there at the moment. Will keep my connection up for about 18 hours with no power.
Hot swappable can be done either of two ways. The unit can have two batteries, where you can pull one out to replace with a fully charged one while it runs on the other, or it can have an internal LI battery that will keep the UPS running for about 30 seconds while you swap the main battery. In any case, you must have a fully charged battery to put in.
If I regularly experienced power outages of 12 hours or more, I would look into disconnecting the internal battery and using a group 27 AGM instead.