The Clawshot is a special item in Twilight Princess. Unlike with other items, Link cannot move normally while the clawshot is traveling.
With L-Slides, though, it is possible to travel a small distance in any direction while the clawshot is moving. These slides can save time, as in Palace of Twilight while clawshotting sols, and can also be used to initiate Clawshot Actor Displacement.
1) Enter first person.
2) Shoot the clawshot.
3) While the clawshot is out, hold the analog stick in a direction.
4) Press and hold L to begin sliding in that direction.
1) Shoot the clawshot.
2) While the clawshot is out, tap and release L, then hold the analog stick in a direction.
3) Press and hold L to begin sliding in that direction.
In either case, the camera will return to third person and Link will slide until the clawshot returns to his hand.