It sounds like you are trying to fix a flat tire on your car without stopping - you want to keep driving down the road without letting your passengers know there is an issue.
Installation of a patch cluster should be done in single user mode - with your system in the state it is in now, any patching should be done in single user to avoid more issues. The patching should not be seen as something you can 'sneak' in to fix an issue. Removing that directory was wrong - no way around it but it happens to all of us at some time. Just get the down time and do it right. If there is a dependent patch, put it on and then try the patch cluster again - it may come up with another patch that should be on before it runs. You must put it on also - until you have it all set. As stated before, this may not be the best way but it's an option.
The best thing you could do is to rebuild your server. Run a backup first and then reinstall the OS and then the applications.
Only you know what can be done - we don't know what applications you are running, the sensitivity of them to your company. You need to insure you don't do more damage in trying to fix your server. Pull over and fix the flat before you crash!