Re: 3.8 Litre Stern Drive options?
There is nothing to worry about as far as the upper gearcase goes, it's lower units that have two service categories.
If you have the original Cobra lower unit with the 13 spline (400 size) propshaft, it is only rated to 140HP, and it would definitely be stressed behind a V6. The early Cobras mated to 4 cylinders used the same basic bearings, gears etc as the 400 series they replaced.
The 400 series was light duty with uncaged needle bearings on the propshaft and smaller. lighter parts throughout.
After 1990, all 4,6 and 8 cylinder Cobra lowers got the same larger case lower with the 15 spline propshaft. (Johnson and Evinrude V4 outboards also started to get the larger V6 outboard lower for the same reliability reason)
So it depends what year and model of lower unit you have.
As far as replacements, you could look for a 15 spline lower, a whole drive from a V6 Cobra, or do the SEI conversion to Mercruiser Alpha
If you don't do a lot of watersports (towing tubes or skis etc) and just cruise, it will probably be fine if you just baby the throttle.
If you have the 2 BBL 3.8, it is only 170HP, so not that far over. If you have a 4BBL, you are 185HP which is getting up there.