There were (still are???) three type of exhaust set ups on the F-Type V6 - no active (ie no valves on the exhaust pipes), plain active (no switch on the console to turn the valves on and off and the valves are effectively operated by the Dynamic button/switch) and switchable active (button/switch on console).
I thought all V6 S came with switchable active but it seems not in your case and you have the plain active version. In which case you can use the Dynamic button/switch as a virtual active exhaust button but this would come with the annoyance of switching between Dynamic and Normal settings for throttle response, gearbox response, steering response and suspension.
If you have Configurable Dynamic this would not be so bad as you could configure it so that the suspension stays in Normal mode even if everything else is in Dynamic (this is my set up) as I find the Dynamic suspension mode to be a bit too harsh for normal day to day driving on the crap roads in my area.
However if your car does not have switchable active exhaust it probably does not have Configurable Dynamic either.
My car did not come with Configurable Dynamic but all it takes to turn it on is a tweak of the CCF (Car Configuration File) using SDD, and I had it done by a gentleman who has the requisite equipment, knowledge and experience.