You may fly the missed approach in NAV, provided the nav accuracy doesn't drop below 1.0 NM.
If it does (likely only if no DME-DME update possible) you would have to go on heading and follow conventional navigation.
I don't think there is a GPS RNAV approach with only GPS based missed approach segment, that would leave you with no option in case GPS failes. Which is possible even with positive RAIM prediciton as it could be switched off or just fail.