You could split it up into two targets:
check-syntax: check-syntax-c check-syntax-cxx
Then check the syntax using the C compiler and the C flags in one target, and using the C++ and C++ flags for the other.
Although you have to split up your sources in C and C++ sources, which you should do anyway.
If you don't have the files split already, you can do it using a GNU Make text function named filter
to split the sources:
CHK_SOURCES_C = $(filter %.c,$(CHK_SOURCES))
CHK_SOURCES_CXX = $(filter %.cpp,$(CHK_SOURCES))