As you know, Frost DKs have a One-Handed Weapon requirement on their core abilities in Legion. Currently the situation is as follows:
If you start a fresh level 55 Death Knight right now, you can't even use most of your abilities as you only have access to a Two-Handed starting DK sword. There are no One-Handed options available from the quartermaster or vendors either.
So until you get to Outland, and unless you constantly switch specializations from Unholy to Frost in order to get a One-Handed Weapon as a reward, you can NOT in effect level a Frost Death Knight without the use of Heirlooms.