Unless they changed it. NOT ALL SHIPS HAVE NAVIGATORS.

Navigators are a prized resource they only use on special vessels. Sure, a lot of vessels got navigators. But far from all.
Like all the bulk freighters.
The imperium would like to have more navigators, but its the navigator houses of the Navis Nobilitae on terra who decide who gets to have navigators. Making it a political danger zone to get hold of them.

Most capitol ships have them, IE cruisers and up. But the smaller it gets the lower chance it is that they managed to get one on the post.
You think that each cobra class destroyer in their battlegroups got navigators? Nope.
They probably managed to get hold of one for the entire group, but not one per ship. If even that.

Many astropaths are actually really crappy, needing whole groups to get any sort of message along the way. And of course the more important a vessel the more astropathic personnel it can acquire.
So a cruiser probably have like 3, with one being the astropath proper. (I might need to check the numbers. Checked them, didn't find exact numbers, Choirs isn't really a good counting system.)

The case is that larger vessels have dibs on astropaths as well. So any skilled astropaths will be moved to more important duties. So this crappy little vessel would logically have only a single not very impressive astropath if even that.

I have no idea if GW effed up the lore even more in the latest edition. But as i remember it, navigators are priced and rare individuals. With the imperial navy needing to keep many vessels in dry-dock or in system since they lack navigators to guide them between stars.

Also JB.
I did not use a real psychic power. Sure, i've used things who are warp touched and would be possible to detect on the warp spectrum by psykers.
But i'm not sure the astropath/'s would be like instantly aware of my use of power and be like "Critical alert, all armsmen to this location."

Urgrugg's and lucius pet psykers shenanigans are however more likely to be detected. Being more far reaching in nature.

IIRC the captain was a self centered douche so he might even disregard the mad ramblings of his astropath since psykers are all insane after all.
I'd say that the mission isn't doomed, i'd wager that the enemy vessel isn't even on alert so far.
But that's just me.