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The 4 ohm speaker in my new/old HH combo is connected directly to the PCB with a little clippy terminal socket thang; easily removed.

In order to make the combo double as a 1x12 cab, I want to disconnect the internal speaker, hook it up to a 1/4" jack and use the external speaker socket; also allowing me to hook the combo speaker up to a head at some point.

Using the external speaker outputs doesn't actually shut off the internal speaker, which makes me think removing that connection (that the internal speaker provides) might cause problems. Sure, it's a hearty amp built to last, but I'd prefer not to take out the output transformer just yet..

I know it's a pretty niché question, but I figured I'd ask; here's a hugeass pic with the aforementioned connections marked out on the PCB:
I guess if all the speaker outputs are wired in parallel, it doesn't matter?

If all the speaker outputs are wired in parallel, you will have no problems disconnecting from the internal speaker socket. Just make sure anytime you turn the amp on there is a speaker load connected to one of the speaker jacks.
If I were you, I'd use a multimeter and check continuity between all of the speaker solder points on the amp board just to be sure.

Multimeter yeeeeah, of course. Gonna have to pick up my own, I'm sure my dad doesn't want me stealing his again.

I wondered if it was obvious from the PCB, it certainly looks like all 3 speaker outputs share at least one connection.