Its a horrible idea if you dont have mw bow mw arrows and mw sword.
^^
No seriously, you dont need heirlooms. I have....lots, cant remember how many, dont really use any, not worth it, use w/e, it wont make you a better play to have better gear. I would beware of this build though, its really tricky to get enough skills as a HA AND anything else, unless you go 15/18 build, and I am NOT belittling your experience or skill but, I personally dont know how much you have, if you have been around for a while, sure do this, but it is not a noob friendly build because unlike pure 1h cav or pure HA, you wont be doing much dmg either at range OR melee if you choose to hybrid. But that being said, for killing off unarmored horses it can be usefull to have some ranged capabilities, so, IMHO go for it, whats the worst that could happen.