Swift only applies to a Main Phase move action (which is when a player pays 2 action tokens to move this character during their Main Phase) and stacks with the abilities of other cards that raise/lower the Main Phase move action cost. The cost to move a character with the Main Phase move action cannot go below 1 action token. (506.3)(609.2b)
This card’s activated ability does not count as a Main Phase move action (which is when a player pays 2 action tokens to move one of their characters during their Main Phase). (506.4)