That does seem like an annoying matchup. Personally, I've always found Shyvana is especially vulnerable to ranged harass (which is why I prefer playing her as a jungler), while Katarina gets to harass non-stop due to her being resourceless. I doubt I could give much experience on overcoming ranged lane harass in general since it's something I struggle with myself, but as an avid player of both Shyvana and Katarina I can at least give you advice for that matchup specifically.
Katarina's auto-attacks do pretty much no damage, and especially at early levels her E and W don't really do any damage either. This means that her Q is all she's really got. If she uses it, it can hurt, and she can and will try to push you out of lane with it, but everytime she does use it you've got about 10 seconds in which she essentially has no damage, so if you pick a fight with her during this window she's gonna take a beating. Though she can use her E to escape, she can only use it so long as she has a target to jump to. Before you engage, take a look at your minimap and see how close your next wave of minions is to arriving. Katarina's next wave of minions will be about the same place. If they're close, this means she'll probably be able to escape if you go after her. If they're far away, then she's not actually going to have anything to jump to to get away from you, in which case go after her. Save your R for when she uses her R to interrupt it.
Another thing is that, because Katarina's auto-attacks are so weak, she'll often be wanting to use her Q to last hit minions. It always bounces to the nearest target when she does this. So try to keep your eyes open for low-health allied minions and stay away from them so her Q doesn't bounce to you. In fact, by staying far enough away from a nearly dead minion, but forward enough to get aggressive, you can try and force her to choose between poking you or getting a last hit in. Regardless of which she chooses, again, her Q will be down for 8-10 seconds depending on what rank it is, which leaves you a small window to try and either do some damage back to her, or chase her away from the lane so she'll lose CS.
Finally, I'd suggest buying an early
if you can. It gives you MR to make her attacks do less damage, while also giving you some decent damage to fight back with, and it's (relatively) cheap compared to most other offensive items so you can get it fairly early.
is very good as well as a purely defensive item, as it pretty much completely negates magic-based poke damage.