An executor should not be needed. The insurance policy can be processed without a probate proceeding. When there are beneficiaries listed on the policy it is known as a non-probate asset. You will need to submit a death certificate of the policy owner and fill out the claim forms that the insurance company will provide to you.
I agree with Mr. Adkins and Mr. Gold. If you are dealing with a life insurance company and that's the only asset of the estate, you may not need to go through probate. You may simply apply for the proceeds from the life insurance company and see what happens.
If a probate does need to be opened, the executor (or administrator) is whomever is appointed by the probate court. That could be you or someone else. You may wish to consult a probate attorney in your area.