Shamrocks and clovers aren't the only things that symbolize Saint Patrick's Day. The color green itself is also highly appropriate for this holiday. As such, there shouldn't be anything wrong with just wearing or having something green-colored on the day in question even if said item isn't shaped like a shamrock.
There should thus be no reason why you can't wear jewelries with a viridian shade even if it doesn't have a clover design or theme. The absence of shamrocks on jewelries won't make the item any less appropriate for the holiday in question. One of the things that makes the aforementioned items a very good gift choice is the fact that you can wear these products all year-round even if the occasion is long over.
If you're just going to acquire some jewelries anyway, it is best to get something that you can wear anytime you want to and not just on a certain day of the year (of course, if you don't mind wearing clover jewelries even if it's no longer St. Patrick's day, that's perfectly fine as well).
So, what are some of the green-colored jewelries, that don't have a shamrock shape, which you can consider giving as gifts or wearing for Saint Patrick's Day?