From my experience, the Weller units are probably your best shot.
The little pen/butane models don't put out enough heat to do much outside. Any sort of wind and most of the heat gets carried off.
I remember trying one of those back in the 80's or 90's and it worked OK if you were indoors, but not outside. I had one that would leak, and blow through fuel pretty fast.
I was in Home Depot the other day and saw that Milwaukee sells a soldering iron that runs off their M12 line of batteries. I'd be tempted to try it, but I don't really need it. I've been running my own personal tools with a couple of their M12 batteries for a long time. Several of the batteries are originals from 2010 and still going strong.
Milwaukee M12 12-Volt Lithium-Ion Cordless Soldering Iron (Tool-Only)-2488-20 - The Home Depot
For work I finally put in an inverter in the truck. That lets me use a decent sized iron out in the field. Add an extension cord and it's worked for everything I need. I can drop down on of the horizontal bin doors on the side and it makes a handy work bench.
I put in a 300 watt pure sine wave inverter so I could run some of the test equipment without issues. 300 watts is plenty for a soldering iron and just about anything else I need. If I need more, I'll grab a generator.