This is a good idea. You don't even need an external SSD, you can use a simple USB drive as well. I've done this for a long time with an old laptop and a lightweight Linux Mint distro (although you can probably have something even more lightweight on there)
Ungoogled Chromium: https://chromium.woolyss.com/ It should be the most barebones Chromium browser, hopefully using less RAM. And! Important: Download the 32bit version, even if you choose another browser. As your friend only has 4GB RAM, the max memory a 32bit software can address, you wouldn't have any benefit from a 64bit version, and 32bit apps usually use much much less memory (RAM).
When it comes to browser options on Windows, your primary options are going to be Google Chrome, Microsoft Edge, or Mozilla Firefox. Firefox works well for me and my needs, but you or your friend's results may vary. There's also browser's like Brave and Vivaldi, that might be worth trying. However, Brave has some crypto stuff, which can be turned off, but may not be for everyone. As for Vivaldi, it's settings can be a bit overwhelming for first time users.