I don't like paper piecing. What I would do is print out a few copies of the templates. I would cut apart the #1 dark blue and #4 light blue triangles first, add 1/4" seam allowance all around them, and then use some common garden-variety triangle rulers to cut those out so they finish to the template size.
I wouldn't cut the #3 light blue/#4 white and #2 dark blue/#1 white pieces apart; I would leave them together with the line running through them.
The #3 light blue and #2 dark blue are just strips, so I would add 1/4" seam allowances and cut strips of the correct width for those pieces. The #4 and #1 pieces are white odd shapes. For those, I would cut extra-wide strips of white (maybe an inch wider than the templates), and then sew a blue strip to a white strip to make a strip set. I would tape the combined paper template to a ruler and place the straight line between the two pieces on the seam. Might be able to cut all edges that way, or might need to use a combination of cutting and tracing to get the shape completely right.
For the #2 white pieces, I would probably cut over-sized rectangles, sew one blue triangle to one white rectangle, then use a ruler to extend the edges of the triangle through the white fabric. Again, I would leave two of the pieces together in the paper template (#1 dark blue and #2 white) and (#1 light blue and #3 white) and tape to a ruler. To cut, I would line up the line between the 2 pieces with the seam just sewn.
I'm sure there are other ways of breaking this block down too. Without doing a couple of blocks myself, I can't be sure which way would be the most efficient. However, it can certainly be done without paper piecing.