Well first up, that's not the heater core, that's the evaporator for the A/C unit. The heater core is INSIDE the car, behind the evaporator box.
And if you just bypass that valve (which you say is leaking), then you will have hot water running through the heater continually. Probably OK in winter, not so good in summer.
Unless you are not bothered by no A/C, I'd either buy a new heater tap which our hosts here sell (as per above), but I do know you can get them from Old Air Products. I bought one from them some years back and it works fine.
Or if you don't want to worry about no heater, just bypass the heater and the heater valve by circuiting the water out of the pump and straight back into the block. You can even just plug each end and have no hoses at all.
Tell us how it works out
Ian
