can i update safari without updating os

Sorry, no. Safari is now considered to be part of macOS and there are no standalone installers. To be on the latest version of Safari you need to be on the latest version of macOS most of the time. Apple does release updates for older macOS versions from time to time but only to patch security problems.

You can always start using a third party browser like Firefox if you are having trouble with websites using an old version of Safari.