My view is likely to be unusual, but unless you plan to tow it around a lot I would not get the trailer. IMHO, personally, I don't like the look of a trailer smoker in the context of a backyard smoker, like sitting on the patio or in the backyard. It looks to me like it belongs in the garage or on the driveway. Plus, the warmer is likely to add a good bit of weight. Plus, the trailer components (tires, wheels, lights, wiring) are going to require extra periodic maintenance for something you're not taking advantage of because you said you're not going to tow it. And, of course, its more expensive.
Since you don't need the trailer or warmer, I would leave them out, enjoy the lower cost, lighter weight, and missing trailer maintenance, and speak with the fabricator about the best wheel options for your needs. I'm sure they have alternatives, and the biggest and best of these will still be cheaper than the trailer + warmer. I've had two stickburners for 25+ years and, although they're not as big as yours, they are very heavy, have very tiny wheels, and are a pain to move thru the grass -- but I've never wished either was trailered. I'll bet the Shirleys now offer much more practical wheel choices.
On the other hand, from perusing this forum in the past it looks to me, as I said, that my views are unusual; most folks seem to really like the trailer look, enjoy or at least don't mind the trailer maintenance, and are willing to accept the extra weight and higher cost in order to have a warmer. If this is you, then go for it.