Yes i you want only for you to have access to the share you can remove the everyone group, but you will have to add yourself to the share permissions, if you remove everyone and don't add yourself to permissions then you have blocked yourself also from accessing it from network.
Also even if you leave everyone group, you can still allow/disallow access to others by NTFS permissions on security tab.
You have Network share permissions which control who can access the network shares and what they can do on the network, and then you have NTFS permissions which actually control who can read/write/modify the files.
If you allow somebody full access on NTFS but don't allow access on network share then you have only given them rights to the files when they are working on it directly from a machine.
For somebody to be able to read or modify the files over network he has to have network and NTFS permissions