Can any deadbolt be made to work without an outer lock?
What you're looking for is easily and cheaply available.  The relevant keywords are "one sided deadbolt" or "keyless deadbolt".  

Home Depot, for example, has a selection of them that start at $7.  

If you already have a deadbolt you want to use, some companies sell a conversion kit to replace the keyway with a blank plate.  Here's one from Kwikset.  However, that's more expensive than just buying a new one sided deadbolt, so I'm not sure I see the point.