No you don't. If you are applying for a vaccine waiver based on religious convictions, all you send in is your AOS papers, your DS-3025 that is incomplete (mine was incomplete as I only received vaccines as a child) which you get a copy of from your CS in Canada you went to, and your waiver with your statement explaining why it is against your religious convictions, possibly statements from family members, friends and/or church members and you send all that together in one package with 2 checks (one for your AOS and one for your waiver) to USCIS. Unless you also apply for AP and EAD (I didn't because the waiver was costly enough!), that should be all.
I was confused like you, it looked like I needed to see a CS here in the USA to just check the box that I would file for a waiver on form 693, but when I called they would only do that if I would redo the whole exam, which is ridiculous since I had it all done in The Netherlands. So I did not file 693 at all. USCIS already has my medical from the US, and the incomplete vaccine record is what I filed the waiver for.
I filed in July and still no green card so I don't have an update yet other than doing my biometrics, but this is how I did it and others before me who had shared it with me.
I am assuming you are missing more than one vaccine?