Make old snow Leopard MacBook safer
Do you have another Mac that you can use to download the El Capitan installer (you should be able to access the link from any Mac running High Sierra or below). Then you can just install it on the old MacBook from there, or from an external drive. Sometimes you have to find ways to work around the roadblocks Apple puts up. But you should have no problem upgrading that machine to at least El Capitan (my 2008 MacBook unibody is currently running Mojave, thanks to a patched version of macOS, but El Cap is the last officially support version for those machines).

To answer your security question, according to Apple’s security updates page: https://support.apple.com/en-us/HT201222 they are still issuing security updates to El Capitan and to the version of Safari running on it, so you should be in good shape as long as you can get your Mac upgraded.

p.s. I’d recommend maxing out the RAM and swapping out the slow spinning HDD for an SSD to breathe new life into the machine. Whatever you choose to run will work a whole lot better with an SSD especially.