This is the right rear wheel.
Do I need a wheel puller, or should this wheel come away from the hub with cautious persuasion?
To remove just the wheel, no.
No puller required, normally it would be loose by now, if stuck, a good solid bump should break it free.
If the wheel has a tire on it, take a hammer and hit the tire on the back side. It should come off. You can't remove the hub, until the wheel is removed. Then you will need a puller to pull the hub, if you want.
In relation to your other question in removing the axle nut, yes you need a puller to remove the hub but you must get that wheel off first.
There are many ways to remove a stubborn rear wheel, a search will find most.
This from a previous post of mine:
I'm assuming you want to remove the hub and not just the wheel?
Here's what works for me:
1. Jack up the opposite wheel (put jack on axle of opposite wheel)
2. remove hubcap, cotter pin & nut
3. Buy a knockoff wheel puller from Langs ($3.25)
and screw on the axle threads all the way
4. Use a 4 or 5 lb hand sledge and give it a couple of medium raps (and NO, 5 raps with a 1 lb hammer does NOT equal 1 rap with a 5 lb sledge !)
Works every time, no danger of buggering up the axle threads or nut threads, and its cheap!
PS Thanks for the tour of your shop!
Bill, it looks like you have a rusty wheel on a parts rear axle. these can be a bear. It will help if you use heat around the narrowes part of the wheel hub, just as you would use heat to free up a frozen nut. Then the suggestions made above may work better for you.
hope this helps.
allan from down under.