Card Boxes at wedding reception

You could have the card box say "Advice Cards" or something along those lines so that people know that is what the box is for.

If I showed up to a wedding, and the couple had explicitly not asked for a gift then I would not bring one with me and would have nothing to put in the card box other than the well wishes or advice cards that you provided. However - if someone still came with cash or gift cards, I am sure they would put it in the box anyways and there is nothing you can really do about that.

I would have a box out for cards as you will want something physical for people to put the cards into. People will at the very least want to give a card - have someplace to place it. You don't have to label it with any words, unless you want to.

In my experience, people are going to give you gifts whether or not you want them. I'd just have the card box, and anticipate at least a few monetary gifts get mixed in with the cards. You might also receive a couple physical ones at the wedding. I personally feel awkward showing up to an event like that empty handed, and will bring a card even if I've already mailed a gift. Without the card box people will just leave the cards on the table out in the open, and I don't know if you want to risk something happening to them.

A thought... maybe you label the box "well wishes & greetings"? or something like that.

I think a card box is appropriate - you don't want them getting lost if folks do end up bringing cards.