My cyclocross bike has a single 42 chain ring and a 6 speed freewheel. I ground down the teeth off a 50T ring to use as a chain guard on the outside and I have a 'half' front derailleur just to keep the chain on in the inside. I used to just leave the FD on and that worked too. You will lose your chain if you don't protect it up front and that could be dangerous.

I am guessing that the safety you are feeling is due to the brakes on the geared bike. Put some brakes on your fixie and come back and see us

Seriously I find a fixed bike feels so much safer in traffic. I used to ride brakeless in a high traffic area now I live in low traffic but still weaving in and out fixed is safer then free imho. Combine that with brakes and you can zoom right up to traffic lights if that’s what you want to do.