All two-stroke (or 2-cycle ... It'll list the recommended oil-to-gas ratio. The oil-to-gas ratio depends on the specific model and engine type. Two common ratios are 50:1 and 40:1.
With a 40:1 fuel/oil mixture the little engine idles and runs as well as a two-stroke can, belching blue smoke and making a ruckus. This answers the question of whether you can build a two-stroke ...
For a lot of people, it's just easier to upgrade to a newer engine, but for those hanging on, there's still some life you can ...