From the author's README on Thunderstore

Early-2000s fitted caps for ReSkate, worn the way they were meant to be: sideways, cocked, tipped up or backwards with a lean.

New Era-style stitching, flat brims and side patches
Holo brim stickers on some designs
Fitted to the game head, so they sit snug without clipping

Where to find them: Apparel > Eyewear. The hats are built on the eyewear slot (the game crashes when a hat item's model is replaced), so you can't wear glasses at the same time.

Installation

Open the ReSkate Launcher
Click Mods
Click Install .zip
Select SpicyTacos_Sideways_Hats.zip
DONE

Known issues

Uses the eyewear slot, so no glasses with these hats.

Install SpicyTacos Sideways Hats

You need ReSkate and your own copy of skate. on Steam.

Open ReSkateLauncher.exe and go to MODS.
Search for SpicyTacos Sideways Hats and click install. The launcher also installs anything it depends on.
Press PLAY. In game, the MODS tab of the ReSkate menu (Insert) turns it on and off.

Or install it by hand: download the .zip and drop it on the launcher window, or unzip it into its own folder in Mods\ beside Skate.exe.

Maps show up in the ReSkate menu's level list. To join a server running a custom map, you need the same map installed. If the game won't load after installing, see known issues.

skatemods doesn't host or review this mod. The download comes straight from Thunderstore. Only install mods you trust, because scripts can run code.