Well, the site you've linked shows teeth and adaptors that will work on your bucket .. but I initially thought you wanted to use genuine original Cat teeth and adaptors. There's nothing stopping you using aftermarket designs or brands. You basically need the cutting edge thickness and leading profile to start with, when looking for adaptors.
That site has some very good info listed under "Selecting the right bucket tooth".
There are bolt-on and weld on adaptors. The weld-on adaptors are generally better in extreme conditions .. but the bolt-on ones are easier to replace when worn. If your cutting edge is already drilled, I'd suggest bolt-on adaptors. If it's not drilled, then weld-on adaptors might be easier and cheaper.
Bolt-on adaptors can be removed when not needed, to save on wear and provide better grading ability. Bucket teeth wreck your smooth grading ability.
The tooth design is related to the material it has to work in .. with penetration ability, impact resistance, and abrasion resistance, being the three primary concerns. The tooth seller will be able to advise you on the correct tooth design for your application. Shale types vary according to locality, and can vary in abrasiveness and hardness. Most shale requires teeth with good penetration ability.