When I make half square triangle blocks I sew two strips or two swatches together then lay the template on the seam and cut out your half square triangle block. You will get an accurate block if you cut accurately.
If you are making a lot of them of the same colors just cut out two strips and sew them then cut out all the squares you can then pull apart the strips and sew the other sides together and continue to cut out half square triangle blocks. You won't have to cut out any triangles as they will show up when you cut the square out.
The waste is minimal if you snug up the template to the last one cut out.
Any waste is well worth the effort for the accuracy you get.