Icarex can be cold cut using a very sharp blade (Stanley knife, etc). Doesn't fray.
If you want to hot cut, yes a soldering iron will do the job very well. Make sure the cutting tip is filed to a fine edge so there is minimal heat bleeding away from the cutting edge. Otherwise you can end up with an uneven cut as heat drifts away from the cut line.
Regardless of cold or hot cut, ALWAYS use a guide or template. It can be a simple straight edge, like a steel ruler. Or curves can be performed against a tin can, metal washer, or the like. You can make a single use template from poster board, but don't allow the melted icarex edge stick to the cardboard for too long.
Hope this helps