The formation of NH4Cl from NH3(aq) and HCl is endothermic, I believe.
I'm pretty sure it's exothermic.
Enthalpy of formation (kJ/mol):
NH
4Cl(aq): -300
HCl(aq): -176
NH
3: -81
So we're looking at -43 kJ/mol.
My source is wikipedia though, so it might be wrong.
Also, I would not really call ammonia and HCl as "safe chemicals", with reasonably concentrated solutions there is plenty of scope for permanent disfigurement. Dissolving ammonium chloride is definitely endothermic, and you'd have to do something quite spectacular to hurt yourself with it.
Also, dissolving potassium sodium tartrate (Rochelle's salt) in water is endothermic. I don't have a value to compare to ammonium chloride though.