i completely stitched my yo-yos down to the background blocks- like an applique piece- so i do not envision having any problems when it comes to laundering---i sure hope anyway- i don't know how they could mess up- they are stitched all the way around.
i've seen lots of toys made with yo-yo's and those can be washed too--
if you are worried about it i would just do a practice piece and see how it goes.