The HC04 should work with the 100k pulldown resistor. If you go much smaller, the HCT04 might be required. If you go below 50k, there is no guarantee either will work, as they only guarantee 50ua of sourcing current when VSS=5v.
Just as a point of interest, I think this part may be PMOS, not CMOS. If it were CMOS, they would have N-channel pulldown transistors on the outputs, in addition to the p-channel pullups.
It might be just as easy to invert the pulse with a transistor. Connect a 10k resistor from the tamper output to the base of a 2N3904 (or your favorite small-signal transistor), 100k from the base to GND, emitter to GND, 10k from the collector to +5V, and connect pin 2 of the 555 to the collector.