Actually the recommended removal technique does involve a trackpump – unscrew first then use trackpump to pop piston out.
"4. Closed 2 caliper
The piston requires unscrewing using a pin spanner. In most situations the piston
will easily unscrew, if it is tight then do not force it with the pin spanner or you may
damage the piston, in this case use the appropriate Hope tool available from your
Hope dealer. Unscrew the piston to the end of its travel, at this point it will rotate
freely without unscrewing any further. Now follow step 5 to completely remove the
piston from the caliper.
XC4 Caliper
The procedure is similar to the Closed 2 caliper described above except the piston
requires unscrewing using a broad flat blade.
5. To remove the piston (all calipers) a bicycle ‘track pump’ is required. Open the
bleed nipple 1/2 turn place the air line over the bleed nipple. Place your thumb over
the recessed transfer hole and ask a second person to apply pressure with the
pump. The piston will eventually eject with some force so point the caliper towards a
clean rag to catch the piston and prevent damaging it. Caution : do not look directly
at the piston whilst carrying out this operation otherwise it can fly out and strike you
in the face."