How is "signal strength" characterized on a coaxial cable?
The SNR used in the Shannon-Hartley theorem is the ratio of the signal power to the noise power. 

So you want to use the power in watts or milliwatts to plug in to the formula.

Of course, if you have the power in dBm, you can convert that to milliwatts.

Or if you have the voltage amplitude (and the characteristic impedance of the system) you can also use that to find the signal power.

In practice, I've seen all of the following used to describe signal powers:


Power in watts
Power in milliwatts
Power in dBm
Voltage amplitude
Voltage peak-to-peak
Voltage rms


You should be prepared to convert any of these to the others to be able to compare specifications provided by different vendors or customers.