Probably Not, but equally Possibly Yes
This is very similar in language to Ring of Spell Storing to which Jeremy Crawford has provided guidance.
Choose a spell of 5th level or lower that you can cast, that has a casting time of 1 action, and that can target you...You cast that spell--called the contingent spell--as part of casting contingency, expending spell slots for both...
Ring of Spell Storing requires:
Any creature can cast a spell of 1st through 5th level into the ring by touching the ring as the spell is cast...The level of the slot used to cast the spell determines how much space it uses.
Both the spell and the item require a spell to be cast into the ring, although while Contingency seemingly includes Cantrips (as less than 5th level), it also stipulates that Spell Slots are expended (which a Cantrip doesn't.)
Jeremy Crawford was asked if someone could cast a Wand into a Ring of Spell of Storing and he responded with:
Casting a spell into a ring of spell storing does require a spell slot.
It requires a spell slot. A wand doesn't expend a spell slot.
The implication with the Ring is that the means do matter and the spell being cast into it must utilize a Spell Slot.
But is this applicable to Contingency?
Basing a ruling from an item and using it on a spell isn't foolproof and may even be foolhardy. The mechanics are similar, but not identical. The intent for the Ring is clear, but that Ring also has to track spell level for the purposes of the Ring itself and how much can be stored in it. It's unclear if Jeremy was referencing that mechanic or the casting into mechanic.
You and Your Table
Given the ambiguity, it's going to likely be up to the Table. Contingency is generally a multi-day spell and burning a resource one Day one that will have been replenished by the likely time the spell Triggers isn't that big of a deal. Burning a resource (1/day) for a racial spellcasting trait seems an equal trade-off, suggesting that allowing this is not a big deal.