You can try to take US-190 around the outer side of Baton Rouge. Traffic on city streets is likely to be more stressful than on the interstate.
The big problem is there isn't a bridge across the Mississippi north of the Baton Rouge US-190 bridge until you get to Natchez, MS. That turns a 315 mile trip into a 460 mile trip.
South of the I-10 bridge in Baton Rouge the next bridge across the Mississippi is the LA-70 bridge near Donaldsonville. Which puts you on the West Bank in the middle of nowhere.
Some might think going through New Orleans and then US-90 across the swamps is a good route. It adds 45 miles or so to the trip. The traffic through New Orleans is never better than the traffic in Baton Rouge.
US-90 is a great scenic drive. It is SLOW, it is frequent stops for construction - and the road suffered several damaged bridges and washouts during the recent flooding.