Signal integrity headaches due to termination and reflections in transmission lines do not depend on the frequency of the signal. The crucial factor is the slew rate (or rise time), which determines the highest frequency in the bandwidth of the signal. Here is a random example from the internet:
Such ringing on the edges may cause one clock edge to be interpreted as several clock pulses by the receiving chip, which will corrupt your transmission. This only depends on rise time, not signal frequency: a 1Hz signal with fast ringing edges can do this too. Edges that are too slow are a problem too. Your 74VHC chip datasheet specifies a minimum input transition rise/fall rate of 20-100 ns/V depending on supply voltage. If the signal spends too much time in the transition zone, this can cause problems.
74VHC rise time is listed as 2-3 ns, which could cause problems considering the length of your cable. However, its drive current is quite low (4/8 mA for 3.3V/5V), which in your case is excellent as the chip's weak output drivers will behave more or less like a "free" source termination resistor which should be sufficient to avoid any problems.
With a 74AC or LVC chip, it would be another story, these would require a source termination resistor.
Make sure to place a decoupling cap on the cable driver chip's power pin. It needs transient current to charge the cable capacitance. Bad decoupling will cause crosstalk through the power supply, or transient supply voltage (and output voltage) sag when many outputs switch simultaneously.
You can check signal integrity at the receiver end, but make sure you use a 10x probe of adequate bandwidth and the tiny ground spring (not the alligator clip lead).
Note that you should probe at the receiver! Signal will be distorted at the driver (pic source):
Voltage at driver side ("A") plateaus halfway between logic levels during the whole time it takes for the signal to make a roundtrip in the transmission line. During this time, line capacitance is being charged, so the driver draws current to charge it. However, signal at the receiver end is clean, and its rise time does not depend on transmission line length and total capacitance (besides losses). This is a bit counter-intuitive, but it works. Driver supply current does depend on line length and capacitance though, as the current to charge the line capacitance comes from the supply.