Can I shoot any approach at an uncontrolled airport in VMC without any clearance?
You would have to cancel your IFR flight plan with ATC, fly the duration of the flight and the approach by VFR, but, yes, you could.

Many people fly practice approaches at untowered airports by announcing their intentions over the CTAF.  This can be difficult to do at beehive airports with a lot of GA traffic going into and out of them, but it’s possible.  I’ve done it plenty of time without incident.