Seal uses a plastic core - Our machine is pretty old, and the inside of the core is getting worn... its been on my to due list to replace it, I'm hoping I can find one that works. Now I have a layer of tape on the inside to keep it tight... it works but eventually wears out, pain in the ass. You're supposed to put a cardboard core overtop of the plastic core though... Cant imagine how many knife marks would be on it if you guys dont!
I much prefer the way our RS holds rolls though. it being reverse wound allows you to also tape up a different web to the same core until it gets really big. We use 5-10 different overlams a day... having to constantly remove the web core is a pain. on our RS, you can just cut...reload, retape, repeat until the takeup core is really thick.
If you dont produce enough cores... you can buy some.
https://www.uline.com/BL_3653/Kraft-Tubes
Any 3" core should work on standard laminators. We recycle 5-10 cores a day...we get so many we dont know what to do with them. You could likely goto most sign shops and ask if they have any they can spare... probably get a dozen or so that way from one of the bigger guys. Just telling them you're making a cat tree and theyre be eager to give them away rather than pay to recycle them