If I have no creatures in the graveyard, do I nevertheless have one Type of creature?
The effect should not apply. You do not have one Type of monster in your Graveyard; you have zero. This would be different if the card said, say "all monsters in your Graveyard are the same Type" - that statement is certainly vacuously true with an empty Graveyard.

Further, it doesn't even matter. The effect only affects monster of the same Type, and obviously none of your monsters have the same type as... the null set. So even if the condition were satisfied, the card would do nothing.

(Disclaimer: I don't play Yu-Gi-Oh; I'm just reading what the card says.)