I use 8mm collets in my Sherline lathe and mill.
Definitely get the headstock adapter.
It would be a good idea to splash out on the WW tailstock adapter and the adjustable tailstock tool holder. With these you can achieve near perfect tailstock alignment and the ability to hold tiny drills. You can also make custom tools like long or half centres for the tool holder. It's a very useful tool and really ups the level of precision attainable.
I also use a collet holder on the rotary table.
Be aware that Sherline make collet adapters in two different types – WW and 8mm. These vary slightly in size of bore. Have a look at the Sherline website for sizes and other details and carefully measure your own collets to make sure you don't get the wrong type. Maybe use your new dial calipers!
Steve