storage near (but not on) cedar?

The big closet in my new place, the most likely place to store my pu'er, is lined with what I believe is cedar. It's not really strong smelling in there, but there is a slight cedary aroma. If it's relevant, the closet doors are slatted, so there's some airflow (I suspect this isn't ideal in general, in terms of being able to control humidity).

My question is... if I store the tea, not ON the cedar, as it would be in a cigar humidor or something, but on wire shelving in the closet (most likely not in a cardboard box or other container), will it pick up too much of the cedar? For now, I've stuffed it in the bottom of my Zekova wood tea tansu, which doesn't have too much of a wood smell; however, there isn't enough space to adequately separate different ages of tea in there, and more generally, there isn't enough room for all my tea down there, so I need another solution pretty quickly. If I used cardboard or plastic boxes, would that be sufficient to isolate the tea from the smells?

I may end up getting a custom cabinet made, but I'd rather not if I can avoid it.