You are going to find that storing anything at 70% RH in a wooden box will tend to suggest wood that has at least some odour. The reason for this is that usually this odour is a result of high oil and/or resin compounds that suppress moulds and maybe even beetle larva, which will be a problem at such high relative humidity.
Furthermore, the wood chosen is rather dense, so we can keep the humidity inside the box. This is different from wood used in the kitchen or bathroom or sauna, where we want the wood to be resistant to rot, but also dry out quickly and not hold onto moisture.
The cedar you mention (which is a misnomer, because it isn't actually cedar or even from a coniferous tree) is chosen because it is relatively close-grained, keeps its oils for a long time, and isn't quite as strong-smelling as other woods used for the same purpose.
At the end of the day only you can decide if your tea is too delicate for this.
I'm hesitant to suggest that any wood would be appropriate from this if what you want is a neutral smell. Maybe using white oak (a classic "kitchen" wood) for the basic box, and then line it carefully with one of the denser, oilier woods from the tropics. I'm thinking of the ebony-like woods with various names, and things like purpleheart.
Though, again, these oilier, more resinous woods do have a distinctive scent sometimes.