I claim the ornamental design for the cardboard construction tool handle, as shown and described.
FIG. 1 is a front perspective view of a cardboard construction tool handle showing my new design;
FIG. 2 is a front view thereof (the rear view is a mirror image);
FIG. 3 is a right side view thereof (the left side view is a mirror image);
FIG. 4 is a top view thereof; and,
FIG. 5 is a bottom view thereof.
The broken lines depict portions of the cardboard construction tool handle in which the design is embodied that are not considered part of the claimed design.