It's a terrible wheel. Seriously, get rid of it.

I'm a nice guy, so send it to me and I'll get rid of it for you, but I'll require a $25 disposal and handling fee.

---

Swimming Workout of the Day:

Favourite Swim Sets:

2020 National Masters Champion - M50-54 - 50m Butterfly

I don't think 13 mm is as narrow as you are making out. Many stock training wheels are either still 13mm or have increased to 15mm in the past 2-3 years. Companies including Shimano have gotten into the habit of listing only a 'rim width' measurement which is a useless metric and you need to look at the rim size i.e. 622-13C to get the info you want.

The disc was probably optimized for an 18-20mm tires, like the Hed Tri-spokes of that era, but you should be just fine with a 23mm. The move to wider rims and tires is about marginal performances differences. That said don't try and stick a 25/28mm tire on the disc.