I’m using a 0.8mm diameter D-shaped tip.
T18-D08 to be specific.

https://www.hakko.com/english/tip_selection/series_t18.html#type_d
However I sincerely believe that for this simple mod, you can get away with almost any tip that is less than 2mm in diameter.
I also believe it is much more important to use an iron whose temperature control you can trust. It should definitely be meant for soldering electronics which means proper temperature control and ESD protection. I recommend soldering at 350 degrees Celsius (plus or minus 20 degrees depending on conditions).
You shouldn’t need to hold the soldering iron to the area that you are soldering for more than 3 seconds.
Pro-tip: When out of practice, or using equipment for the first time (new iron, new tip, or new solder), practice making a few solder joints on a PCB that you don’t care about. This is where you set temperature and adjust technique so that you are able to wet a good solder joint in less than 2 or 3 seconds.