Using two tires on one wheel to prevent punctures?
I'd just buy tyre liners (example from Zefal).  They're made from tough polyurethane which many sharp things won't get through or at least not quickly. I've used cheap (unbranded eBay) ones on a cheap bike when I didn't want to buy expensive new tyres, and they worked well, with one issue, probably what your mechanic was thinking of that was easily solved by taping over the end.  They can be cut down to fit your small wheel, and it looks like the ones I've linked are made wide enough. Another popular brand is Mr Tuffy, though I've never used them.

If you want to try recycling instead of buying, then use the tyre liners as inspiration.  Here's Zefal's video on fitting them, so you can see the approximate proportions.