Be quick with your jumps
When you swing, make sure to jump pretty quickly. Not right away, because you don't want to mistime it, but do it soon enough. Because if you hold on and just keep swinging, you'll lose velocity, And when you lose speed, you can't pick it back up so you'll need to drop.
Hopefully, you're in a position where if you fall, you won't die. If that's the case, then you'll more than likely land on a trampoline which can get you back up and swinging again. This will let you reset and prepare for a jump. Be ready to launch yourself to the next grabbable object.
Some levels will require you to do this several times while the earliest levels are extremely easy. You'll likely get more comfortable with jump timing as you progress. You'll just need to adjust on the fly as each level changes more and more.
Earn some silly new characters
Yup, that's right, there's more than just our friend Mr. Stickman. You can unlock some new characters while you play. There are others you can get for free too. In this game or any game really, it's always fun to have the chance to play as some different characters (unless it's a game where you create your own).
You can get silly characters such as a panda, a ninja, or even a hot dog. It's always enjoyable to switch things up and give yourself a fresh new look. And the more you unlock, the more options you have so you probably won't get tired of changing.
So this is nothing more than a preference hint. Adding personality to your game can enhance the experience, even if it's just a tad bit. And no, picking the ninja won't make you swing faster or jump higher, unfortunately. Sorry to get your hopes up there.
Feel free to use only the trampolines
Be wise about this, but if you see that the path to the finish line is easier by just jumping on the trampolines, then, by all means, go for it. You can bounce fairly high on them, and they are normally near each other, but it depends on the level overall.
If you want to play it safe, then just continue going back and forth between trampolines and hooking objects. Just bouncing and not using the hook could be a good way to simply challenge yourself too. Sitckman Hook is still a pretty casual game, so you can have a little fun and test yourself too.
But, it's all up to you as to how you want to approach a level. If you do die (which you won't early on), then just learn from it and practice your jump timing on the trampolines if that's the route you feel that you need to go.