Tyvek is HDPE, not PTFE. I'd be concerned about the solvent permeating in any case. I don't think there's any great way to use standard mason jar lids with solvents other than water. The liner on the ones I get starts peeling after a day or so of ethyl acetate vapors, definitely not good. Mycology suppliers have one-piece polypropylene lids that look potentially good, though I've never used them. PP lids with a silicone gasket are easier to find. The silicone might swell some, but I doubt it's a significant issue. I don't have the analytical facilities to say for sure, but I'd guess any leaching is both small and well-rejected by the crystallization.
A properly fitted ground glass joint seals pretty well, and the standard taper is slight enough that it almost but doesn't quite self-lock. A wrap of Teflon tape may improve the seal and discourage seizing. That seems like overkill here, though. Lab suppliers have borosilicate glass bottles with a thick PP cap (like the GL45, though I prefer smaller), optionally with a PTFE gasket. They also have thick PP bottles that are good for some solvents (e.g. ethyl acetate) but not others (e.g. DCM). As noted, check the compatibility tables.
I wouldn't worry at all about contact with PTFE, unless it's something that might shed fibers, shavings, etc. I also wouldn't worry much about brief contact with a silicone stopper, and I'd certainly prefer that to my hand!
As to the original question, the toxic hazard from solvent fumes here should be negligibly small with adequate ventilation. Professional chemists work with much nastier stuff in open beakers with no respirator, relying on their fume hoods to control both the toxic hazard and the explosion hazard. This is an example of the general principle that engineering controls are better than PPE--it's better to quickly exhaust the fumes than to let them accumulate and then try to protect yourself. I feel good when people say they're wearing goggles and gloves, but nervous when they say they're using a respirator--are they needlessly cautious, or are they quickly approaching the lower explosive limit?
I work outdoors. If I couldn't then I would improvise a hood. It's still a good idea to keep large containers away from your workspace to reduce the severity of a fire, but that shouldn't noticeably change your toxic hazard unless your ventilation is inadequate. I expect that improved ventilation or safer solvents (e.g. limonene) would decrease your toxic hazard by more than any other measure.
You consistently blow me away.