Universal presser feet sound like they should work on every sewing machine, but this is not necessarily the case depending on the type of shank adapter they use. For example, Singer has their own proprietary low-shank and slant-shank adapters, which only work with Singer brand snap-on feet. In addition, the attachment bar on their shank adapters is a bit skinnier than the ones you see on most other brands. Hence, a universal presser foot is unlikely to work with their machines.
For the sake of optimal safety and functionality, we recommend buying presser feet made for your specific brand of sewing machine. Presser feet that are not fully or correctly secured may pop off, which can result in serious injuries for your child. Furthermore, it can damage the machine, thereby ruining your child’s projects, and possibly voiding your warranty. That’s why it’s best to follow the manufacturer’s recommendations and to ask them about compatible alternatives before purchasing any replacement parts.