I have already read a warning that trying to replace one of these
torsion springs can result in injury or death, so we'll have to call
someone.

Lowes & HD sell replacement parts, including springs, for garage doors.
Just raise the door all the way up to take the tension off the springs,
wedge a board under the door so it can't drop, then replace the spring.
If it were me, I'd replace both of them. The warning you mention is a
CYA by the manufacturer to protect themselves from idiots.

Bob S.