NEMA 10 series is depreciated, (banned for new installations since NEC 1996 edition) as they do not have a ground pin. It is likely that a rework station originally fitted with a Schuko European plug has a three wire cord and requires a ground for safety. IMHO unless it has a two wire cord, your stepdad is correct and fitting a NEMA 10-30P would be unsafe. The heater insulation of these Chinese rework stations is often questionable, so I wouldn't trust one with mains voltage heating elements and a two wire cord anyway!
Its also worth noting that the max rated current for any European socket that can take a Schuko plug is 16A, so either that 20A fuse isn't original or the manufacturer bumped up the rating because they were getting nuisance fuse blowing due to inrush current.
A way forward would be to refit the circuit for a properly wired NEMA 6-30 outlet if you don't have any equipment that needs the Neutral for 120V control circuits, or get a ground to the outlet somehow and fit a NEMA 14-30 outlet. Rather than fitting an over-rated plug on the appliance use a NEMA 6-30P or 14-30P to 6-20R adapter.
If you cant refit the circuit with a grounded outlet (e.g. rented property), for private use you could make up an adapter with a separate ground wire which *MUST* be permanently connected to a good tested electrical ground. Don't let OSHA see it!