I was looking through Q&A on EPA site and it doesn't look like EPA actually keeps registration info for certified technicians the numbers may be provider specific. One of the questions was about lost certificate numbers and all the answers pointed back to whoever provided certification. Skillcat does show up as approved organization though so am sure it's valid.
There is no "standard EPA number", because the EPA does not issue certificates or monitor whether or not a certificate is valid. cgrutt spelled it out. The EPA approves testing facilities that give out their own certificates with numbers they make up. Their certification of you is their testimony that you passed their testing regime, which was EPA approved. You are responsible to maintain your records of your certification, because the testing company does not file your records with the EPA.
The EPA 608 certification allows you to work with and purchase refrigerant so there's no reason you wouldn't be able to purchase it. Most HVAC supply houses require a commercial account so that can be a PITA but there are plenty of online refrigerant sources. I've used Royal Refrigerants a couple of times and have found their pricing and service to be excellent.