For curlies who straighten occasionally, do you still co wash before flat ironing?

I always have to have freshly washed hair prior to flat ironing. When I use shampoo, I can only have my hair straight for about a day and a half before it starts to look greasy. I feel like co-washing would make my hair greasier even faster. I want to co-wash before straightening so that way I don't feel like I have to add silicone products just to get the shine and 'moisturized' feeling that my curls have when I co-wash.

Also, if anyone could recommend a good non silicone heat protectant? I haven't been able to find any whatsoever ):