Disabling safe mode or removing apps from safe mode

I use a Droid 3 which has not yet been rooted. I need to remove access to the Browser or the Play Store. I already have an app called "program encrypting" which disables access to selected apps unless the user has a password. However, when the user enters safe mode, all downloaded apps are disabled, allowing the user to use the Browser and the Play Store. I am curious if it is possible to disable safe mode in some way, or changing the button combination to enable it. I would also be fine with removing those applications from appearing in safe mode. I am new to rooting and such, and I would appreciate being able to remove access to these apps in the safest, quickest way possible.