I think it would be better just on the base as well without edges. It's not like the hard plastic toys are made of and probably wouldn't be good to chew! It does cut really easily though. It's mainly the wood base you want to protect. It's not that cheap though - I bought A1 sheets for my playpen - bought quite a few though and it came to about £25.
You can get one really big sheet here for £16 and cut it to size.
https://www.ebay.co.uk/itm/Correx-Sh...4AAOSwq4VaMT3V