You don't need to use the widest aperture. In fact, in many cases, using the widest aperture for astrophotography can result in very poor quality stars. If you are doing wide field untracked imaging (i.e. milky way imaging), then you can usually get away with using maximum aperture, and the larger aperture allows you to use shorter exposures, which reduces star trailing.
If you are doing any kind of tracked astrophotography, it's usually better to stop your lens down a bit to sharpen stars up. With tracking, you can expose for many minutes, so being able to use the fastest aperture is not as important. The impact to star quality from CA and other aberrations can be quite extreme with many lenses, so stopping down for quality becomes critical.
For example, few astrophotographers using 50mm-100mm lenses will use them wide open when using some kind of tracking, as the stars get horrible blue or purple halos around them. Most of the time, a fast 50, even an f/1.4, will usually be stopped down to f/4 to get better, tighter stars and better vignetting. For astro, f/4 is still quite fast in the grand scheme of things, where telescopes at native focal length are often f/8-f/11.
As for what aperture to use. Focus with stars doesn't require deep DOF. The stars, for all intents and purposes, exist at the same focus distance, since they are effectively at "infinity." You can get away with focusing at f/3.5, or even f/2.8, if you have to. The thiner DOF makes it more challenging to acquire focus, but once focus is acquired, then there isn't anything else to worry about. Because of the extremely low light levels, you would not want to use f/16 or f/22...that would just be wasting photons. However, apertures between f/4 through f/8 are acceptable, although even f/8 is kind of pushing it. You shouldn't need to use apertures that low unless your slapping a 2x teleconverter on an f/5.6 lens. Usually stopping down a third of a stop is enough unless your using a very fast lens, (those faster than f/2.8), in which case stopping down to at least f/2.8 is better, and f/4 is usually more ideal.