Could I get an current iPod Touch and downgrade it to iOS 10? Assuming that it comes with 11? It isn't an elegant solution, and is a crass stop gap that doesn't really solve the problem of developers abandoning apps.
Yeah, it doesn't solve the problem but a stopgap can be worth it if you have some app you really depend on or just like a lot... it lets you use the old apps until you find out for sure if the developers are abandoning apps for which no 64bit version was available on launch day of iOS11. Or use them while you try to round up some substitute that runs in iOS 11.
I don't know if I'd go as far as buying an iPod Touch and downgrading it but since iOS 11 is officially only days old then it's likely all the refurbs and even the new ones are still on 10.3.3.
iPod touch still sells in the refurb and clearance section (16GB and 32GB only) for $129 and $169. It's possible they are just running down the stock and they're not even refurbs, just new and being unloaded (if the rumors are true that the line is headed for discontinuation).
I've never had a problem buying a refurb iOS device. if you get one, they're like new, certified by Apple with a year warrranty and even eligible at point of purchase for the AppleCare extension to 2yrs coverage if desired.
The iPod touch that Apple still sells new (32GB and 128GB only) are $200 and $300. You have to click on "Music" at the top of the Apple home page to see them though. That sale location seems like another sign that they could be headed to end of life as a product line... or at least not being emphasized, to cut down on cannibalization vs assorted iPhone models including refurbs. Those probably would come with 10.3.3. on them too at least right now. It's not like there's so much demand for this device that the stock is likely to be hot off the assembly line.
All that said, the problem with trying to keep an old iOS and 32bit apps going, no matter the hardware of the mobile device, is going to be finding reliable (e.g. safe) copies of 32bit apps if you don't already have them on your laptop / desktop. Maybe the devs would help you out if you don't have what you need. If you haven't upgraded iTunes to 12.7 and do still have the apps you want and don't update them via iTunes 12.6.x then you still have them available for sync "the easy way". If they put out a security update on an old iOS like 10.3.3 to secure operations of older devices like the 5th gen iPod touch, that could be a problem, but you'd just have to make sure you didn't update any apps, just the iOS.
I won't be using the older iPod touch that I have my handful of 32bit apps for anything but using those particular programs going forward. Once I find substitutes for those 32bit apps then the device reverts to use for something fairly static like an audiobook server or local music player. Or the kid down the road finally gets relatively lucky with a hand-me-down piece of gear yet again. Whatever he's using now is probably a still older version of iPod touch if I remember correctly and he only uses it for music too. The nice thing about Apple stuff is it does last a long time. I still have a bunch of 2nd gen nanos that just won't die...
