Similar story. I too suck at shooters; yet (after having become obsessed with this game) I'm now a lvl 37.
The only other shooters I've spent considerable time with are the Uncharted games (which often focus on adventure more so than kills).
So, I was as reluctant as anyone. I had never even played the first Splatoon. That said, I'm so glad I took a gamble on this one. It's phenomenal.
As for your concern about being able to keep up online, I can almost guarantee that you'll greatly enjoy yourself & claim victories in no time. Remember, you are always going to be on a team! The matches are 4 vs 4, so you either win as a team or lose as one! And given that you are a bit tentative to equip a gun, consider using a non-firearm-variant instead; perhaps one of the rollers or brushes will appeal to you more. Or, even a gun that gets great ground coverage, so that you can focus primarily on stealth & thoroughness, letting your teammates focus on getting the Splats (kills).
Hope this helps!