The general answer is no, mainly because weightlifting shoes are specifically developed for extreme lifting movements that put tons of pressure on the feet. The focus with weightlifting shoes is to keep the lifter stable on the ground while providing extra heel support (many of them have raised heels). Wrestling shoes, on the other hand, tend to have thin, flat unisoles or split soles that focus on grip and flexibility.
Having said that, a few companies such as Otomix makes shoes that can be used for both purposes. We chose to go with Otomix because the materials, construction, and design are clearly appropriate for wrestling. Furthermore, their shoes have been approved by countless wrestlers and coaches, as well as athletes in other combat sports such as kickboxing and mixed martial arts (MMA).
Regardless of which brand shoes you choose for your child, make sure to look for the following elements: enhanced ankle support, flexible sole and superior grip/traction. Once those requirements are met, you can choose based on your child’s personal needs and preferences, such as material, dry-fit lining, reinforced side panels, etc.