Can you use greaseproof paper or baking parchment instead of waxed when making items involving royal icing?

Yes, either greaseproof paper or baking parchment can be used instead of waxed paper for drying items involving royal icing, but you will see a noticeable difference because greaseproof and parchment paper are thinner than waxed paper.

Depending on the project and the weather conditions, you may need to let them dry for a longer amount of time as opposed to if you had used waxed paper. This is mostly needed for items that you can't hang such as cookies. But if you're making things like wreaths, garlands, gift toppers, etc., hanging them to dry is recommended no matter what type of paper you use to allow air to circulate all around them.