Squier skinny body question.

[BrianToska]

This is my first post on here so I apologize in advance for any ignorance of proper TB etiquette.

I recently received a Squier Vintage Modified Fretless Jazz Bass for free through a friend of mine. I've tried for a long time to give fretless a try but it's just not my thing. So my solution to this problem is obviously to get a new neck. I've considered a Mighty Mite neck with maple fretboard but noticed that the Squier body is thinner in depth than my MIM Fender Jazz. My question is, Will a Mighty Mite neck fit properly onto my Squier without any major sanding or modification? I've searched the forums and googled it and cant seem to find anything about this. Maybe its just because I'm a newbie :P

Thank You in advance!!