hard steel

Most likely yes.  You would be better off using a brass rivet to attach the handles.

The other question would be what material were your taps?  I had a cheap set long ago, and couldn’t cut threads in something (probably an automotive repair).  Happened upon an acquaintance who was a factory machinist, and he told me to get some High Speed Steel taps.  I did, nearly choking on the price at the time, and tapped the hole easily.

Jason

Check the surrounding steel with a file.  If you can file it relatively easily, you can tap it.  As Jason said, get a high speed steel tap, and be sure it's sized correctly for your pilot hole.  If the file just skates across the surface, forget trying to tap it, as the steel is to hard.  In that case, use a brass rivet as Mike said, or use a small screw and nut, with the screw sized to go through the hole.  Sometimes free stuff is the most expensive !

Don't dispute the fact the handle may be hardened like the operational end of the tool but I disagree on saying HSS taps are harder and guaranteed to do the job. A certain HSS tap may be harder than a certain carbon-steel tap but a carbon-steel item is capable of being harder than HSS at the penalty of being more brittle (likely to break if you aren't careful).

Any tool that hard is almost certainly brittle. Much like a file it could shatter like glass if you get a catch.

It is I fine balance between toughness and hardness and I would be afraid of someone else’s homemade tool.

Crazy people used to make scrapers out of old files generally it did not end well.
 
Walta