It doesn't make any sense to cross-compile the designer plugin for the target platform, when the designer is not intended to run there ( at least you have disabled the designer itself in your Qt build ). Edit qwtconfig.pri and disable building it.

From the INSTALL file:

qwtconfig.pri and qwtbuild.pri are read by all project files of the Qwt
package. qwtconfig.pri is also read by qwt.prf, when building your
application. So the first step is to edit the *.pri files to adjust
them to your needs.

Uwe