It really boils down to what works best for YOU. Of course you can cut the diagonal and chain stitch. I do this all the time with my leaders and enders. I do scrap pieces all the time this way as well but what I do is trim down my HST after it is sewn to make sure it is nice and squared up. As you already have your squares cut you probably don't have much wiggle room for squaring up unless your pattern had you cut the squares oversize. A way to tell is if there are instructions to square them up after sewing or if the squares were a 7/8" measurement.
There are so many ways to make HST, from triangulations to grids like Jan posted and the way your instructions say. However I would definitely eliminate drawing two lines and only draw one (or you can fold your square in half on the diagonal to put a crease in it) and sew 1/4" on each side of the crease or drawn line. In my mind it is a waste of time to draw two lines and sew on the lines. That is why we have 1/4" feet!
Edited to add, Quilting is not a race. Sure there are techniques to streamline the process but sometimes the better results are achieved my slowing down and taking your time. I would try it the way your pattern indicates and try it the way you want and then measure your finished HST to see which method gives you the more accurate result and do it that way, even if the more accurate way is more steps and takes longer. In the long run you will be much happier with the rest of the process of making the quilt and the final results.
Last edited by feline fanatic; 02-15-2016 at 06:51 AM.