Can I update apps without going to the new operating system?

Yes, upgrading to 64-bit shouldn't have any effect on Mojave. Unless the apps require Catalina. You can check app compatibility here:

https://roaringapps.com/

BTW- all Apple apps are already 64-bit and have been for many years, the apps you are talking about are third party apps

Unfortunately, the only safe option anymore is to double-check. Find a forum, like this one, and ask specifically which apps are safe to update. You will need a list of the apps you are running and their versions.

In some cases, they might not work on an older operating system. In theory, systems like the App Store may prevent you from updating some updates to an unusable configuration, but not always. And sometimes, people can copy apps outside of the Mac App Store.

And in other cases, a minor "update" might require a subscription or have significant new bugs. You just can't assume it is safe to blindly update.

New or changed Apple apps may only be compatible with Catalina, so use caution when trying to update them. Check that the update doesn't make the app incompatible with Mohave.