Whitelight, I apologize for having not responded to your direct request for input. I wanted to have the time to sit down and write while not rushed. As I write my response there will be little inserts so that newer shooters readers don't get lost.
As you stated up front, the lowest numbered aperture (largest opening) is ideally best to allow the most light you can. However, your question about using f4 is actually more relevant than I knew until two weeks ago (and not for the reason you were asking). As photographers we are all trying to learn and improve our craft. Two weeks ago I attended a seminar on night photography with my daughter. The entire time my daughter kept beating me up to go, "dad you know all this stuff." Which was true, and then I stumbled upon a golden nugget of information relative to aperture. The speaker started to talk about how ideally we want to use the largest aperture we can, but we need to do a little examining of our aperture to figure out what that best aperture is.
At this point he put two pictures shot on the same full frame Canon camera while swapping out lenses. The first lens was a Canon wide angle of professional grade and the second was a considerably cheaper Rokinon wide angle (Sorry I can't tell you the models of any of the equipment as it wasn't important to the lesson or me). He then zoomed into the outer "squared" circle of the two pictures shot at we'll say 1.8 (whatever the widest was for the two lenses). The stars from the Canon lens squared circle area were actually shockingly bad at 100%. Speaking in plain language, the center of the stars were white, but the edges of the stars really suffered from other colors showing up on the edges of the stars that shouldn't have been there. The Rokinon, at the same aperture and 100% zoom had little edge color bleeding into the white of the stars. The presenter was actually quite surprised at the difference when he first noticed and investigated.
The presenter continued to raise the aperture number (smaller opening) and showed us the diminishing edge color bleeding. I do not remember where each came to its ideal star aperture number, but the Rokinon achieved an ideal star in the squared circle at a much lower aperture than his Canon lens did.
To your original question, what are you going do with your pictures? If you are only displaying on a computer then fire away wide open. If you are going to print, and you are shooting wide angle, you want to print big. The compression of a wide angle just doesn't do the print justice unless you go big because you're stuffing too much into a traditional sized picture.
Which now brings me to finally answering your question after all my long windedness, and this is what I am going to do this Friday night on my Milky Way shoot (clouds permitting). Shoot a number of photos starting at a wide open aperture. Then, incrementally tighten up the aperture and shoot again. Of course you will need to play with ISO and exposure time. Once you have these shots sit down and compare the squared circle of your images and see what the stars look like in this area.
Once you know where the aperture sweet spot is for stars on the lens you're shooting then you can start to play with how long of an exposure vs ISO to avoid noise and star trails. However, Milky Way photos are all about the editing and noise reduction. Photoshop has been my tool of choice and I have done really well with it. I have recently started playing with Nik Tools and the noise reduction tools are amazing. Combining the two, Photoshop and Nik Tools, I believe I will be able to push my Milky Way photography to a new level.
As to star trails and avoiding. The wider the angle of lens you're shooting the longer you can expose before trails will start to show. You can also push that a bit by what you will do with it. If you print larger poster sized prints (I do) star trails will readily show up. However, a more traditional sized print will hide it.
I hope this has helped and I have answered your question; even if I didn't answer it for the reason you initially asked.