How to remove/unlock the passcode of iPhone w/o Restoring?

Recently I set my iPhone 4 to "no passcode" because I let my 4-year-old daughter play with it. Somehow or another she managed to set a passcode on it and neither I nor she have any idea what it is. I desperately don't want to restore it because I live off that phone and it has a ton of work information that I need to keep. How can I unlock it fully without knowing the passcode?
(I'm also backed up onto iCloud, but I have no idea how to access that information. I'm not backed up onto any computer. Whenever I bought apps I did them off the store on the iPhone.)

Your gonna have to restore it through iTunes. There will be a back up option when you do it, so all the info that was on it the last time you synced it will be on there. Same thing happened to me… It sucks

You need restore it.

Just share my experience that when i forgot my backup password, i have opted for the tool - "Tenorshare iPhone Backup Unlocker" to help me remove my iPhone backup file password and get my lost valuable data efficiently.