I suppose it's one of those "on the one hand... on the other hand..." scenarios.
Scenario 1 is you do your own heater core R/R. The big thing here is it's usually a very-involved process. The labor estimator books state it's a 5.2 hour job. I'm looking at the actual R/R shop procedures, and you have to remove the entire dash, and disconnect the refrigerant lines and heater line quick-connects to pull the HVAC module assembly out to access the core. This means draining the coolant (easy), and emptying the A/C system (not easy, scavenging refrigerant requires special tools and very expensive shop equipment, releasing refrigerant in the atmosphere is illegal).
On the other hand, putting it in the hands of a mechanic is going to be very costly (see labor hours above) and you have to trust they know what they're doing. The best choice would be to find a trusted and competent mechanic in that case.