Last year 353 people applied for the 347 tags in the regular random draw for 1st choice, odds of getting a tag are good but not a solid 100% if last year is any indication. Assuming they do not change the tag numbers that's still 98% odds.
Looks like you could apply in special for 2nd choice, draw the tag and still gain a point if your looking at that option.
Area 10 with B is not part of the general tag, so keep that in mind. The website shows some walk in land that might be worth considering. I've hunted antelope in that area but didn't see any deer in the sage, deer on public seemed close the the wooded hills (at least for public land).
If I were to plan a region B tag I would study the WY game and fish website. Find the units that have the most suitable habitat for deer, look at harvest rates then study access to the public land. Arriving a day or two before it opened would allow you to mark off pre determined spots and get a feel for the camping rigs/potential pressure.
I would also shoot for opener. Yes, temps could be warm (or blizzard) hunter pressure will be greatest and mule deer that time of year are hard to find. But, you'll also get first dibs. Season might open on a Thursday so pressure might be a little low for the first couple days, then fall off drastically on Mon/Tues.
I suspect local hunter pressure will be greatest around Casper/Gillette but don't let that deter you, everyone thinks that way.
The walk in areas can be a little gem. People are lazy and want to hunt and glass from the road. If you can find a walk in area or even a state/BLM or forest spot that requires a long walk in before sunrise you could be into something.
Also, public land cover adjoining a private food source (irrigation land) could be a gem too. Of course, the harder it is to get too the better the hunting will be.
With Onx and other technologies thinking outside the box is not as effective as it once was. However, people are creatures of habit.
Your biggest hurdle might be figuring out which roads are open and closed.
Good luck and please keep us informed on how the hunt goes.
If you have a specific area in mind I could look at it and give my opinion. Ive hunted and killed a few mule deer in that type of country but OnX images might be outdated or the trac might have a billion sheep on it when you get there.