Tuffsaw is certainly the place to go, but you may have to manage with 1/4 inch unless you have guides that can cope with a 1/8", as they are very narrow. The 1/16" is not available as far as I am aware, but a special guide would be needed if you could get one.
I managed with a 1/4" for some time and although I tried the 1/8" I broke a few and smashed the curf, so think about it seriously. Depending on circumstances and your bandsaw, a special guide is available from the USA, but is expensive and not all bandsaws are catered for. These are made by a firm called Carter Industries and If you Google Carter bandsaw guides, you will see the range they have . Their price of their Stabilizer will turn out double once you have added shipping and import duty, but do try the Tuffsaw blades first.
Malcolm