Frame data for Ice Climbers' jab:
Total: 29
Hit: 4-7
Window of the backswing: 3-29
IASA: 16
Backswing starts: 14 (or later)
"IASA" means "interruptible as soon as", which means that frame 16 is the first actionable frame. However, there are limitations on what moves you can use to interrupt jab before the animation ends. You cannot perform another jab, grab, shield, or any "B" move during the jab animation. The first two are because if you input another jab ("A" or Z") any time before Popo retracts his hammer, you'll just perform the second part of his jab sequence ("backswing").
What you are doing is simply waiting until the last frame (29) before performing the grab. And you're right--you could be doing it at least 13 frames faster.
Things that can interrupt jab include tilts, smashes, walk, run, jump, and crouch. This means that if you want to perform a move that is not directly actionable during the IASA frames, you have a few options: perform one frame (or more) of walk, run, crouch, or jump, before inputing the desired action. Each of these actions will take you out of the jab animation early so that you can perform another move.
If you want to perform a standing grab, you can input one frame of walk, crouch, or jump, followed by Z. If you want to shield, you can input one frame of walk, run, or crouch, followed by L or R. If you want to jab (rather than finish the jab combo/backswing), you can input one frame of walk or crouch, followed by A (although if you don't let the control stick return to neutral, you'll perform a tilt instead).