Mikkel, translations will not be erased.
BUT, make sure to back up your site first. I recommend using "Data Exporter" plugin for this and just in case do a back up using "Back up" tool provided by your hosting company in your control panel.
>>And is it just to push update and cross fingers for it all to work as before? :)
1. Make a back up.
2. Deactivate all of your plugins
3. Push "update"
4. Cross your fingers and wait...
5. Once update is over, start activating your plugins one after another. Check your site after activating each plugin. This will help you to identify which plugin is causing errors on your site ( if any).
6. Once plugins are activated, check whether there are any plugin updates available.
7. If needed update your plugins.