The issue here is going to be clearance between the frame and chain in the extreme gears. The smaller chainring moves the chain down towards the front crossmember, but from the images I've found online I don't think that will be a problem. The drop from 30T to 24T alone gives you a 19" bottom gear. In order for the rear derailleur to keep working you need to keep the gap between the biggest and smallest chainrings about the same, but you are planning on that anyway - right now 52-30=22T, you want 42-22=20T so that's fine.
At the back you have the issue that you need to clear the frame with the bigger cog, but you also have 10 extra teeth worth of chain involved. The jump where 11-30 becomes 11-40 might not work with your current derailleur, or might not allow you to use all possible gears. I suggest getting a 12-34 cassette instead, as the 11T cog wears out faster and the extra tooth will help you keep the rear derailleur happy. With 34T instead of 30T you get a slightly lower gear without going too far for the derailleur.
If you don't install extra chain, you probably won't be able to physically get into the 42-40 gear, and the drivetrain will wedge itself solid if you try. That can damage the trike, either snapping the rear derailleur off or bending it into the rear wheel.
But if you add the extra chain the opposite happens - in the 24-11 gear you have so much chain that the rear derailleur can't take it all, and you end up with chain dragging on the ground. If you run over the chain the rear wheel will stop and you'll slide along on the chain, wrecking a section of it.
Note that quite a few recumbent riders do this, because the gears where this is a problem are not really useful gears. It's generally better to have the extra chain, because you can shift back out of the bad gear and keep going, but if you wedge the drivetrain it can be annoying to fix even if you don't damage anything (often requiring you remove the rear wheel, or release the boom so you can slide it back and loosen the chain enough to free it).
You will also need a few tools do to this, specifically a chain breaker (and some extra chain links), a cassette removal tool, and some allen keys.
I suggest contacting Catrike first, as they will know exactly what you can do with the trike, and likely sell you the parts for about the same price as an online shop would. Then you can try taking the trike to a bike shop if you have one nearby, or start watching youtube videos showing people changing cranksets and cassettes. All the bike bits like gearing work the same on your trike as on a bike, they're just in different places. So all the instructions you'll find online should help, you just have to remember that "the bottom bracket" is actually out the front :)
Answers here like "is my chain too long" will give you ideas about how to work out the correct chain length after you've made changes. Some of the answers on "cross chaining" talk about why those gears don't matter (they duplicate other gears from different combinations of front and rear cogs).