If I didn't have an original I'd buy one of the Umarex airsoft versions and try it, it really is more comfortable to shoot. Looking at the picture vs. the one sold for the .22 they look similar to me. I haven't ever seen an airsoft version in real life so I can't say for sure but it sure looks close and I have to wonder if they'd make different molds for the two different guns. As they're both HK licensed copies and supposed to look and feel the same I also wonder if they may have used the same housing but with different innards.
The .22 version is rigid hollow plastic with the metal sling fixture adding weight; I don't have my calipers handy but it looks like it's maybe 3mm thick. I have handled a couple of airsoft MP5s and the GSG and yeah, they definitely felt softer and cheaper; it's been a while since I handled a real MP5 with a fixed stock but I recall the stock feeling like it was a little softer material but heavier and more robust than the Umarex sold for the .22.
It's not like the gun has much recoil and the blow back action is contained within the housing so I can't imagine much stress being placed on the stock. We used to have a member here who had a thing for putting various .22 actions in airsoft housings. He had a thread with a large, rather impressive looking collection but some folks were of course making fun of him and I haven't noticed him posting in a while.