I understand the batteries in the HC are 3 AA? that would be about 1.2v x 3 in normal state, or 3.6v
an individual li-ion rechargeable is about 3.6 volts... but completely different charging circuit is normally used.
You would need to at the least study the charging circuit's operation, but most likely it would not be appropriate.
You could purchase a charge control board that would go between the battery pack and the HC that would shut off overcharging, but this would take some experimentation. It's in the realm of do-ability for a person with electronics knowledge and measuring tools.