Steve, a BIG WELCOME to the GTA forum and family.
Yes, safety first....build yourself a spring compressor. Take a look in the "Library" here....there's a few threads on how to build one.
In the GTA Library....I believe there's a thread or a few on how to take apart an air rifle...specifically a spring piston rifle. I did not go there for my lesson/info....I went to Pyramid Air Guns website...over there, there's a 13 part series/blog (Short and easy read) on how to take apart, clean, deburr and lube an air rifle by Tom Gaylord - Pelletier. I read the whole series twice and attempted my first "home tune"...and it wasn't hard at all.
Good luck in the tune. Btw, some of the upgrades you can put into the Big Cat....GRT III trigger (If the original is a metal trigger (If it's plastic...the GRT III might not be a drop-in)), Telsa or Apex piston seal and a Jim Macarri spring...and some of his heavy tar on the spring and Moly paste on contact points (Don't over lube though).