Accepted answer
Stated carefully, the arithmetic only stops being confusing once you work it through once and see that it is straightforward.
Number of stopper piercings matters less than the gauge doing the piercing. A 30G or 31G needle through a butyl stopper leaves a track that reseals; a 21G or 18G drawing needle punches a core and can drop it into the solution.
Breaking it down further: if a 10 mg vial has 96.5 per cent content, you have 9.65 mg of peptide. Divide that by 2.00 mL and your concentration is 4.825 mg/mL, not 5.00 mg/mL, which is a 3.5 per cent systematic error in every dose calculation.
Published data on syringe dead space quantifies low-dead-space designs as retaining under 2 µL against 35 µL or more for conventional detachable-needle syringes.
The limitation is that technique reduces risk, it does not remove it, and nothing you can do outside a controlled environment makes a non-sterile preparation sterile.
Do the arithmetic twice, ideally with someone else doing it independently.