Heat gun, even a hair drier on high heat should handle that unless its really thick stock.
Just cut the shapes you want, a solid pair of scissors will do it. You can always glue layers of thinner card together rather than trying to fight trough cutting thicker stock.
Anyways- cut your shapes out. Then, to get the wavy curves in them, get a couple of pencils, screw drivers, or whatever you can find thats round and wont melt- put those under the card stock and space them out a bit. When you heat the card up- it will soften and if it doesnt start to droop on. its own you can push it down gently between them. A few practice runs with some scrap pieces should get you the results you need ot get some good wavy cruves