Sounds like you’re making good progress on your oven, even if you’ve built a little something extra into the mortar.
I think you’re right. Theoretically they would be in a sealed space if your stucco shell is perfect, thus denying oxygen to the wood as it heats up. Nevertheless, the mortar and firebrick are your primary lining for the oven, and having a combustible material in place of the refractory mortar is not a good thing. The closest reference I could find is to chimney construction, where a double course of bricks and a fire-clay lining are required and nothing combustible is allowed within two inches of the chimney.
Are the wedges accessible? (That is, do their faces still come out to the surface of your joints?) If so, I’d recommend starting with a masonry chisel and a hammer (you’d kill a woodworking chisel and you don’t need the precision) to dig out as much of the wedges as you can, then a shop vac to suck out all the debris and dust. You may be able to remove all of it using just these tools, or pretty close. Then, mix up another batch of refractory mortar and point it into the gaps left where the wedges were. Remember to mist those gaps with water before you add any mortar! You want the new mortar to have the best chance of adhering to your existing work.
That’s going to set you back a few days, but it’s definitely not worth it to just leave them in there and hope for the best.
Good luck, Joel, and keep in touch!