What would the approximate cost of replacing the heater core and the heater core hose be for a 1994 Honda accord EX?

It is not going to be cheap. The heater core itself and hose are not that expensive, but the labor costs to replace it are steep, due to the time needed. This repair is very labor intensive. The price will vary greatly depending on who repairs it and where you live. My advice is to call around and get some estimates. Be prepared to be shocked by the estimates you get.