Can you bypass a heater core in a 1969 Chevelle?

Yep, it's really easy, just find the two water hoses which go into the firewall, below the blower motor on the passenger side, remove the clamps of both hoses, then cut a 5 inch piece of a broom handle (wooden), slide both hoses over it, tighten the clamps and it's done, now you could do this with really short hoses, or even block the passages leaving the engine with welded caps to make it look neat.

good luck