Don't know why the name Culebra but in 28 yrs visiting the island, I haven't seen a single snake there, if you find one, it may be the local non poisonous puertorican black snake, it'll be more afraid than you for sure.
As for dive operators, I don't know who operates from the island, but I know there are 2 dive shops and probably some other operators in the island so diving from Culebra should not pose any problems at all.
I usually embark my diving trips from Fajardo (PR east coast town) and return to Fajardo for the drive back to San Juan.
My favorite operator is Sea Gypsy Chartes, it departs from Villa Marina dock in Fajardo and will take you to some good dive sites, will have sodas and snacks all day long and on the way back (after diving has ended) to Fajardo rum and beer if you like. Cptn. Hector "Tito" Angueira is a PADI instructor and very profesional in his operation.
You can reach him at 787-383-8066. If you buzz me, I may be able to tag along and dive with you if you wish.
Enjoy the beautiful Island of Puerto Rico and the very pristine Island of Culebra.