The holders you are talking about open quite easily. Just slip a knife into the seam of the two pieces and give a gentle twist. This will start the separation and you finish with your fingers.
But you may wish to consider joining NGC instead. They will accept submissions in the original holders and will remove the coins for you for $1 each. You also get the same 4 free submissions
Of course if you decided to join the ANA - you could submit coins to NGC WITHOUT paying the membership fee

And 1 year's fee to NGC or PCGS would pay 3 yrs worth of membership dues to the ANA. And you get all the other benefits besides