Looks like to me, in your case, you can close the vise all the way, wire brush the paint & rust off the slide, spray a little oil on the slide and get it apart.
IMO: It's very important to remove the slide & nut to properly clean the inside of the body for your restoration.
This is a little extreme. Pictured below, I had a Prentiss vise with a cracked slide. Because of the crack, the end of the slide was .110" wider than the rest of it. Using my floor jack and a dead blow hammer, I removed the dynamic slide.