Remove the ends of the two hoses that connect to the heater core under the hood. Then look through the carded Help! or Dorman brand items at the local parts store and you should be able to find a hose connector that is 3/4" or 5/8". I'd use the larger 3/4" and force the smaller hose on, but you might also use the smaller 5/8" and just clamp it a little tighter. Just connect one hose to the other, which will bypass the core to see if that is the source of the leak.
If you find that the leak stops and you want to continue to bypass the core, you have plenty of time until it gets cold again. Changing a heater core on a square body is a little easier than most other vehicles, but still a PIA. There is one last nut (or bolt?) down low in the engine compartment where its hidden by the inner fender, but most others are easy to remove. Its usually easiest to just unbolt the inner fender and let it drop loose to get access to that bolt. Then the other difficult part is getting the inside housing back into place and pressed up against the firewall while you put the nuts on from the engine side.
FYI - I changed the heater core on a 2000 Ford Expedition and the first step was to remove the entire dash, which was one large assembly that ran all the way across the truck. It had all the electrical wiring for the dash attached to it. Of course to get clearance you had to remove the complete console and drop the steering wheel first. It took me almost a day and a half, but was much cheaper than paying the 10 hour labor estimate by the dealer. All that labor to replace a core that was only about $100, IIRC.
Bruce