In theory, yes. In practicality, probably not without an outbreak. The skin on your fingers is too thick too penetrate, and unless there was an outbreak present, there probably wouldn't be enough virus to infect you even if you had a break in the skin.
Most herpetic whitlow cases are autoinocculation, where someone newly infected without antibodies to protect themselves from infections in another location, touch an outbreak with a finger with a cut, or dental professionals from their patients with oral herpes.
This isn't anything I'd worry about at all.