First of all: Why make your hashtags invisible? Simple, to put as many as you want without covering the main content and avoiding a spammy look for your story.
If you use hashtags in your stories you increase your chances of being featured for the hashtags you use, which ultimately boosts your exposure and can get you new followers and engagement. Here's another way you can use to easily boost your engagement.
There are two ways to do this, choose your favorite:
Coloring the hashtags the same color as the background
- Add a hashtag to the story
- Position it in a place with a solid background
- Highlight the hashtag as text
- Tap on the drawing pen icon
- Drag the pen across the screen, as close to the background of the hashtag as possible, until the hashtag matches that background

Putting the hashtags under a big sticker
- Add all the hashtags you want to the story on top of each other
- Choose a cool sticker and put it on top of the hashtags
- That's it!
Easy, no one will ever know you are using hashtags!