Heater Core??

Backstory....About three years ago I ordered firewall gaskets in anticipation of pulling off the heater core, greasing the cables, etc. In the fall I drained the coolant, looped the heater hose to bypass it so I could work on it in the winter which never happened. Well, three years later when I took the car out of winter storage I drained the old coolant and reconnected the heater. When the thermostat opened up so did my core I think. I have a puddle on both drivers and passenger wells. No carpet in the car so it's not a big mess. Does this sound like the heater core? Does anyone have any advice for disassembling the box? I'm dealing with a 51 year old heater box that I'm sure is pretty fragile. Also, if it is the core, where should I order a new one?

Thanks