Hello Sarah,
Short answer, it shouldn’t be any real issue bringing both (beyond you and your caregiver/husband physically bringing them).
First, make sure your flight tickets are flagged for “wheelchair assistance” so they know you’re coming with one. When you are at baggage check-in they will want information about your walker and wheelchair (especially if a motorized wheelchair), and possibly tag them with a special handling tag at this time.
Next, a couple questions:
-Is your walker a collapsible type?
-Manual or non-collapsible motorized wheelchair?
Assuming your flight is from the US and/or connecting to a stop there (or country with similar airline rules: These items should fall under necessary medical equipment and thus not count toward any bag limit. You can use them right up until boarding (wheelchair users board first, so be early, i.e. at the airport 3-hrs before flight minimum).
If both walker & wheelchair are collapsible, then you/your caregiver can fold them up, possibly bring them on board and stow them like carry-on luggage (usually the stewards will help with loading them). This is probably the most ideal situation if you want to control who’s handling your stuff.
However, if either of them aren’t collapsible or too big to fit in-cabin, then you can still use them right up until boarding. From there you will take any parts that detach with you into the plane to stow (so they aren’t lost), and the rest will be taken from there and put into the plane directly (usually the last to go in, and first to be offloaded at your destination). This should minimize the chances of it getting lost because it doesn’t have to go through the underground labyrinth of conveyor belts to get to the plane like luggage does, ideally just traveling a short distance between the passenger door and cargo door.
While I’m sure the likelihood isn’t zero, I’m fairly confident that if you load your items this way that they shouldn’t be lost during your flight. Logistically, it may be more difficult to haul around walker, wheelchair, and multiple pieces of luggage to the airport and/or hotel, so you may want to pack light.
I have written some other tips you may find useful in my blog post Yokohama Life: What I Learned Living 90-days in Japan with a Disability on Accessible Japan, at the least I recommend checking out the latter if you haven’t already.
I hope that helps, but feel free to ask if you have any additional questions and we will try to find you an answer,
-Justin