Yes, you can get by without the mixing valve. Instead, you can use a technique common amongst technical scuba divers (and perhaps others) called partial-pressure blending. In other words, you could begin by carbonating your beer to the appropriate level with pure CO2 from the CO2 tank you already have. Then, once the beer has the appropriate level of CO2 you switch over to a tank of pure nitrogen.
As an example, if you determine that you want your stout to have 1.5 volumes of CO2. So you figure out what the appropriate CO2 pressure is to achieve that carbonation level, given the parameters of your system. Let's just say that's 10psi. So you set the CO2 regulator to 10psi and allow sufficient time for the beer to carb. Once that's done, take the CO2 gas line off the keg and switch over to the nitrogen line. Now your stout faucet produces additional back pressure in the line from it's restrictor plate, so the pressure that you'll have to set the nitrogen regulator at will be significantly higher. I'd start out around 25 or 30 psi and see how it goes from there. You can adjust up or down as necessary. The pressure of the nitrogen in the headspace of the keg will keep the CO2 in solution, and the beer will actually take up some of the nitrogen too. Beer doesn't absorb *nearly* as much nitrogen as it does CO2, but it will take up some. So now you've got CO2 in the beer as well as nitrogen, and you're pushing the beer with higher pressure nitrogen which will overcome the inherent back pressure from your system as well as the extra back pressure from your stout faucet's restrictor plate and give you the nice creamy head you desire. If you're particular about hitting an 80/20 split for the gas in your beer then you would set your nitrogen regulator at 40 psi (since you set the CO2 at 10 psi). But I typically use a bit more of a guess work approach and get the pour the way I like it, rather than obsessing over getting an exact split of gas.
Sorry for the lengthy, geeky post. But this is one area where my love of beer brewing and my love of scuba diving run together.
Brian