I don't think it is nessesary to have the opponnents deck made in advance.
Simply have all cards aside in proper order. Like type and then name.
When ever a card is played, that need to stay on board you simply find it and put it down.
If the card is instant, just seeing it on skype should be enough.
For hidden enchantments, simply put a placeholder facedown until revealed.
If you don't have enough copies of a card. you could use a placeholder sleave with a note on. However this might give away whats in your deck. (perhaps put the placeholder in your spellbook off camera instead)
I haven't tried it, but it seems doable.