GM was pretty good at making parts generic with provisions for options to be added as they were needed.
Both options mentioned, swap covers & the foam between the frames, or taking the easy entry cable & lever from the one & adding it to your existing if the attachments for such actually do exist within your original seat, would work.
Personally, I'd swap the covers between the frames without messing with that easy entry system.
Once installed, cycle the release 10 or 12X just to make sure all works as it should.
A dry lube, such as a teflon-based bicycle chain lube, works well to keep that cable running smooth. A wet oil-based lube has the possibility of leaching onto & permanently staining the cover material.
The cover will fit over that stub for the release handle. Do not cut the hole for that stub until the cover is installed on your original frame.
Either tap the on the material where the stub is poking up under the new cover material with a small hammer in order to break the material for the hole, or cut a small 'X' over the stub to let it poke through.
Do not cut the material for that hole until the cover is installed.
While the covers are off, check the seat pans for twists &/or bends + all mounting points for cracks or breaks in that tin.
Check & lube the tracks while it's all apart, too.
White lithium.
Remove the seats by removing the front floor bolts first, then sliding the seat all the way forward to remove the rear bolts.
This way, with the tracks at the back of their travel, the seats will stand up by themselves on the bench.
Done the opposite & they'll be flipping & falling all over the bench, fighting you the whole way.
Electric seats are heavy & are very frustrating to work on with the tracks all the way forward. Need a 12v power supply & some jumper wires to move them into the proper position.
Manual seats have a big spring attached to the tracks to pull them forward. With the seats removed rear floor bolts first, that spring is under some pretty hefty tension. Hit that release, intentionally or by accident & the spring will slam those tracks back so hard & so fast they will cause some serious damage to the digits if they happen to be in the way.
How serious? I worked with another upholsterer for years that was missing the end of the first finger on his right hand at the first knuckle after a set of tracks caught it when accidentally released.