Yes you could try truing yourself, but also yes you could "destroy the whole thing"! Well, not destroy it, but end up with a wheel more out of true and maybe some damaged spokes. Out of any repair on a bike this one is one you need to get your head round first and take your time on. Don't let that put you off, just take it slowly and carefully and it should be fine.
Here are some things from my experience:
If you have an old wheel you can practice on, that's a good idea to get a feel for the process.
You don't need a truing stand but it makes things way quicker and easier. If you belong to a club or can get to a cycling community meetup, chances are you can borrow a stand or even find someone to get you started. If you can't get a stand you can use your frame and / or brakes as a guide. (The wheel will need to be off the floor so you can spin it).
Make sure you lubricate the nipple thread before trying to turn it. Some people may disagree but I always start by spraying some lube down into the thread. Take care not to lube the tyre or brakes...
If you have bladed spokes keep in mind you'll need to keep the blade in line as you adjust.
If you do round the nipple, you can replace the spoke, but this is a fair bit more work and it's better to avoid it. It's painfully easy to round the nipple, so as people have said in the comments, make absolutely sure you have the right size and decent quality wrench.
Do make small adjustments, but also remember to reduce the adjustments you make as you get closer to true. It's easy to go too far and come out the other side! Start with quarter turns, then eighths, etc.
If from all of that, online videos and tutorials, you feel like you're happy to do it, the answer is yes you should give it a go.