Is it possible to make my game run client side only?

This is an answer that has both side true, both yes and no. Depending on what you are doing you can make this a client-sided only game but if you are going to change any values then you have to use scripts. If you are only doing things that only the player is going to be doing client side (such as clicking on GUIs but without it interacting with the server) would work.

In other words, you can but if you want to change anything that everyone else sees then you have to use scripts (which are server-sided). Depending on what you are doing I would recommend fixing that lag issue with your scripts (it could be because of many scripts running at once). Otherwise, you can come here and we can help you fix them (through attempts).

If you have any questions or issues, please contact me. ;)