What is the kid's average? at that weight the core isn't really the biggest concern, at 12-13lb most company's use a generic weight block that is close in characteristics to the original, but below that even with the same core shape the RG and differential are so different that the reaction will be completely different.
If the kid is using a 10lb house ball move him/her up to at least 12lb, a properly fitted ball won't feel as heavy as a house ball. I'm sure it will feel heavy at first, but using it every week they will get used to it.
Way back when I went from a 10lb house ball to a 14lb fitted ball, yes it felt heavy, but I'm glad i did it.
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