If I have equipment attached to a unit already, can I pay the power cost to unequip it from that unit and attach it to a new unit? Neither unit is a weaponmaster.

No. You cannot pay the Equip cost to reattach an equipment that's already attached to a unit — even to move it to another unit you control.

While equipment is attached, its printed rules text (including the Equip ability) is inactive (Rules 718.2, 135.4). You can't activate an inactive ability. The only way to move already-attached equipment to another unit is via an external effect like Weaponmaster, specific legend abilities (e.g., Jax), or cards like Angle Shot / Relentless Pursuit that explicitly move gear (FAQ 730, FAQ 9593).

If you want to re-use that equipment, you'd need to first get the attached unit killed or otherwise detach the gear (e.g., Strike Down, Veiled Temple), which would recall it to your base — then you could pay its Equip cost fresh during your Main Phase (FAQ 11093).