Soldering-iron sculpting
Ironing isn't smoothing an existing surface using the nozzle, it's extruding a very small amount of material very slowly with very narrow line widths to fill in all gaps and make it flush with the tip of the nozzle. When using a handheld tool like you suggest, you are not adding material, so you have to 'smear' the peaks of the ridges into the crevices evenly, which is going to need to be very close to the print temperature of the PETG. This is going to be incredibly difficult to do without ruining the print, and harder still to do it well enough to look nice or come anywhere close to replicating the appearance of ironed surfaces. Doing so would require someone to be very skilled and have hands so steady that they're NIST traceable.
Sand-and-fill
If you want good-looking results with PETG, the method that gives the best results among hobbyists and professionals alike is the sand and filler method.
It's more work than using a soldering iron-type tool would probably be (assuming you were able to channel the ghost of Michelangelo himself to do it properly, of course), but the results are achievable by anyone and consistently so.
This process is similar to ironing in that it both smooths AND adds material (filler). Sanding is to flatten the peaks of the layer ridges, and the filler is to fill in the valleys.
You sand (using proper sanding technique) as long as you think you could possibly need to, then sand like 2-3 times longer than that. Then, spray the part with a thin coat of acrylic lacquer spray. If you sanded enough, it will look amazing. If not, you wait 48 hours (60 is even better) for the lacquer to fully harden, and then you repeat the whole process again. Sand, sand, sand some more, then sand even more than that, and spray another coat of the lacquer on. Depending on your sanding efforts, this can be done with just 1 coat, but it can often require 2 or sometimes even 3 coats, worst case.
Once it's smooth, you can sand (yes, more sanding) to taste. It will usually be glossy from the coat, but a once-over with medium grit sandpaper can give you a matte or satin finish depending on grit (start with 1200 grit and slowly move up to rougher/lower grit paper until you have the finish you want). Or, if you want smoother, you can start with 1200 grit and work your way down to 1500, 2000, 2500, and 3000. After 3000, if you really want a mirror finish, you can switch to a polishing compound. Any metal polish that works on brass (like Brasso or diamond pastes) and a soft rag, along with lots and lots of rubbing (if you weren't sick of that already from sanding) will get you there.
