I use the same group of blood samples to extract DNA by two methods. In my opinion, I think i shoild use the paired t-test for compsring the two methods. However, the ethics comittee of my university has rejected this idea.
Independent Samples t-test is the way to go because it checks the difference between two groups. Since you are extracting DNAas two different ways, they are going to be your two groups.
Take this technique with your proposal to your supervisor and they wont reject this time.