Can I use Shadow Rider Calyrex VMAX's "Underworld Door" Ability if there are no cards left in my deck to draw from?
Yes, you can. Attaching Psychic Energy is the main effect of the Ability, which means it can be used even if you have 0 cards in your deck.
Source: Chilling Reign FAQ; TPCi Rules Team (2021-06-17)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH6_75
SWSH6_75