If you use a cardboard box, I'd recommend taping it all around, so if your liner leaks your mold won't start to leak as well.
Parchment paper works well as a liner as mentioned by others.
About HP and cure, yes it needs just as long a cure as CP. It is safe right after cook, but definitely not cured.
I use baking paper. Don't use Glad wrap - it will get too hot. I've always used baking paper - we can only get freezer paper here from the craft store where they use for patchwork or embroidery or something. They sell it by the metre - about $5 per metre I think it was. I thought she meant $5 for the whole box at first and thought - wow that's not too bad! LOL. Once I found out the cost I decided that my baking paper ( at $3 per 15m box) was more than sufficient.