Since it was going to take Malak half a year at minimum to secure a license for owning the spaceship, He decided to let her use his license and vouch for her.
That's because he couldn't wait that long due to an issue in the timeline.
If he still recalled properly, the Shurima Temple was going to be discovered by a pirate crew in less than a month from now if the timeline remained the same.
Hence, his reason for rushing everything and not having enough time to plan a better method to sneak Erik and Malak out of the planet without relying on a wish.
As for vouching? It simply meant he would be using his license to give them access to planets and space worms expressway.
Since his criminal record was sparkling clean, they would be given permission right away. The latest incident had been settled properly and wiped out of Felix's criminal record.