In HYSYS Steady State, for a long time the valve would only work with a specified pressure drop. However, as of version V7.3, there is a check box on the Design / Parameters page. that will make the valve calculate the pressure drop as a function of valve opening and valve characteristics. You should be aware that for an imposed inlet flow and pressure, it is no always possible to calculate the outlet pressure. If the flow is too high, the valve will be choked and in steady state it will not solve. If you specify the upstream and the downstream pressure, it will always solve for flow.
In HYSYS Dynamics, the valve has always defaulted to solving by using the valve opening and characteristics. If in a particular case you would want to force a fixed pressure drop, that is possible using the check box on the Dynamics Specs page. And in some special cases it may be useful to uncheck both of the check boxes there to give you the freedom to specify something special. Say that you wanted to bypass a fixed flow around an equipment. You could put in the TEE and Mixer and a valve in between and then add a flow controller to get the flow that you want. But if you wanted that flow to always be exactly what you wanted, you could make one of the streams in the bypass flow specified and uncheck both check boxes to give the solver the necessary degree of freedom.
HYSYS let's you specify Cg or Cv and if HYSYS detects a gas feed it will use the Cg by default, but noting stops you from flipping the radio button on the Rating / Sizing page back to Cv. Most people would feel more comfortable specifying a Cv as it is usually what you find on a data sheet. There is no problem using Cv for a gas valve, so fee free. HOWEVER, if you have a valve with a high pressure drop with the possibility that the flow goes critical, it is useful to consider what the Cg stands for:
Cg is a measure of the critical flow of a valve and C1 (Cg = C1 x Cv) will define at what pressure drop you will achieve critical flow. So, whether you use Cv or Cg, it will be good to also have a look at C1 and check at what pressure ratio you reach critical flow. The rule of thumb is that you reach critical flow is dP/Pin = 0.5. To match that closely, you need a C1 of 26.85, HYSYS has a default C1 of 25, which brings you pretty close.
You might be interested to know that when you switch the "Valve Manufacturer from "Universal Gas Sizing" to any of the manufacturers (not the simple k-value), you will get the option to use the ANSI/ISA formulation. In that formulation the relationship between Cg and Cv is: Cg = 40 x Sqrt(Xt) x Cv. The default value of Xt is 0.7, that makes a C1 of around 33. So, your valve will behave somewhat different when you switch to this formulation.
You can find all this info in the HYSYS documentation and I also found the a PDF document from Emerson Process interesting.