Your post is rather confusing. As I see it, premix is petrol and oil mixed together, not to be run through the pilgrim pump. Two stroke premix oil is oil not premix. Two stroke premix oil like Castrol 2T can be run through the pilgrim pump but is a bit too thin for what the pump was designed for. It is better to run a thicker two stroke oil through the pilgrim pump. I use Silkolene Classic 2T premix oil which is sae 40. There are other 40 grade two stroke premix oils available. In the petrol tank I run a 50: I mix using outboard engine oil, ideal in the Scott as it burns very cleanly, is intended for watercooled engines and has good anticorrosive properties.
This post will probably cause some argument but I have used this combination for years now, with no smoke and no problems.