If you do Xubuntu you'll really want another 128MB of RAM, because with 256 you're still going to be hitting swap every time you run a program. Puppy Linux could probably do what you want, but by default there's /no/ security on it: you run as root without a password; possibly you can install a password and a user account.
Damn Small Linux has security by default, but it's more limited than Puppy. Don't know if it can do wireless printing, and since it uses the old 2.4 kernel series, it may not support your wireless card without ndiswrapper. I run it on my Pentium-90 with 64MB of RAM and it runs acceptably, so performance-wise it should be good for you.
Both DSL and Puppy are LiveCDs but I've heard of people running them from USB sticks, and so you can try them out before installing.
Slackware? It's pretty customizable without having to compile like Gentoo.
With a weaker box like that, I'd use Abiword and Gnumeric instead of OpenOffice. You'll still have to use OOo for presentations. Also make sure to install powertop and use its recommendations, to save power.
i7-8700K|Asus Z-370 Pro|32GB DDR4|Asus Radeon RX-580|Samsung 960 EVO 1TB|1988 Model M||Logitech MX 518 & F310|Samsung C24FG70|Dell 2209WA|ATH-M50x