Blendshape and skeletal animation

I have very simple animation playing on my character:

e1821d48d6c62dcc493f0de467cca7b1e1b4055d.jpeg

Now it is all fine, until I apply blendshape, which makes my character - for example - larger.

Then I get something like this:

corrupt.jpg

As you can see, hands are very oddly stretched. Its like skinning information is not consistent with new blend shape vertex position. Any idea, how to handle that?