"the signal I'm trying to count has quite a slow Tr and Tf of about 600ns."Are they the 10% to 90% times. From the note underneath it looks to me that if you have fast 0.5V to 1.5V times and a good gnd you'd just about get away with your 600ns, it's a bit of a grey area.
If this device is used in the threshold region (from VILmax = 0.5 V to VIHmin = 1.5 V), there is a potential to go into the wrong state from induced grounding, causing double clocking. Operating with the inputs at tt = 1000 ns and VCC = 2 V does not damage the device; however, functionally, the CCLK and RCLK inputs are not ensured while in the shift, count, or toggle operating modes.74HC14 or 74HC132 if nand is useful.