I have two little rug rats running around, a 6 yo and a 1.5 yo, so I see where you are coming from
webMistress.
The Solo sounds like it would work well for you, it is the only vaporizer my wife will touch when I'm not home. You can preload the stems and cap them, so when it is time for a session, just power the Solo on, let it heat up for a couple minutes, then slide the stem in and start sucking. 12 minutes later, the Solo shuts off automatically and by that time you should have a spent bowl. Pretty simple.
If during the session you are interrupted, the Solo can easily be hidden with the stem still in place, as long as it has no chance of something hitting the glass. And if you really need to, the Solo can go with you from room to room.
The only thing that concerns me is your Asthma. The Solo does have a lot of resistance, it is nothing like hitting a normal bowl. As long as you let the vapor flow and don't try to force more pull than it lets you, you might be fine.
I prefer my E-Nano hits when I have the time (flavor and size), but the best results come when the e-nano is preheated, which may or may not be a problem for you. Sounds like you could leave it on the shelf and crank the heat when needed. I'm loving the nano, much simpler and less bulky to use than my SSV.
Choosing just one is a tough choice.
Maybe the Lotus would be a good choice, it is on my to try list. Cheap price, instant vapor, portable, and is easily adapted to a water pipe. Speaking of water, with your condition I would suggest budgeting for a small bubbler. The
cheap $30 D020 would work well with any you choose and is pretty small compared to other bubblers.
Good luck on your choice. Keeps us informed. I really hope you do convert to vapor, not only for the smell but for the health reasons and conservation.