I really don't think lawn ferts would be advisable. We tend to dose Nitrogen and Phosphoros as well as potassium which may be in some ferts (sulphate of pot ash for instance), but generally I think you'll find they'll contain a lot of other chemicals which I don't think would be very good for fish health. I don't think its worth the risk.
As for your sand, you could consider some sort of root tabs under any plants. These are generally slow release capsules that dissolve over time (anything from 2 - 6 months depending on brand) and release nutrients directly to plant roots. Even with a planted substrate in my tank, I still have some of these under my crypts as they are heavey root feeders.
Tropica PN+ root capsules and API root tabs are two common brands.