How can I best hide these screw heads? Wood filler probably will crack...
Consider to remove the screws and perform a counterbore or use a forstner bit to the depth of the screw head. Select the diameter to match your selected wood plug diameter. Return the screw, glue in the plug, sand the plug flush.
You can purchase a wood plug cutter, sort of a hole saw without a center drill, and cut your plugs from the same wood, for a better appearance match.
Places like Lee Valley, et al, sell hardwood "buttons" or "plugs". For shallow holes there are even stick-on veneers, but it looks like you need a proper hardwood plug, either store-bought or home-made.