When I got married cash gifts were pretty common and honestly really helpful as we were fitting much of the bill on our own. Those cards that unexpectedly showed up in the mail helped an awful lot.
It may seem less secure but sending cash inside a card is a reasonably common thing to do in the US. Snail mail is slow, but still pretty reliable and a nice card adds a personal touch that a wire transfer doesn't.
If you're terribly worried about security, consider sending a wire transfer to a trusted local family member and mail them the card with an envelope and so on. I'm sure someone you know will be attending a wedding shower and would be happy to pass along your card and best wishes.
For those that think gifting cash is thoughtless, impersonal, or in poor taste... Think about all the expenses and stress involved in planning a wedding and getting started as a young couple. Cash is exactly what they need, so stop it.
So... Go down to your local grocery, pick out a nice card, write something sweet in it, insert cash, and mail it. Or nudge a family member for a little help if you're a little paranoid.
Another more endearing approach could be to call around to local florists in the couple's area and see if any of them do "money trees". Yes that's really a thing... Usually small bills folded into oragami flowers and/or leaves clipped onto a wire frame tree. This will likely put you a little more out of pocket, but they look pretty, and it may be a nice touch for folks who care about that sort of thing. (Pro-tip many young couples could probably use the extra cash more than the presentation, so consider that when making your choice.)