How do I get to the secret stash of guns without using the speech challenge? On this character I haven't been using charisma at all.

you dont.

If you no clip through the bars you will realize they are just static props and cant be picked up.

You can access the secret stash, but you will need to get various items from various locations. Those items will let you pass the speech check even if you have a charisma of 1 and no skill points in speech.

What you will need :

1. Party time mentats. You will need 50 science skill to make them. If you dont have that you will need to find a way to raise it to that level. Maybe some clothing article, magazines, etc.

2. Moonshine. You can find it in goodsprings, the owner usually sells it as well, otherwise you will need to make your own with that companion Cass, but to get that companion i think you will need to pass speech check again.

3. Wine/Scotch

4. A speech skill magazine. You should be able to find them at various locations.

5. Naughty nightwear. Ironically you will need to buy it from mick and ralphs lol.

6. Mentats. You know where to get them.

Consume, wear all of these at the same time, and then you should be able to pass the speech check.

Edit: Now that I remember it, i might have taken a skill BOOK as well, I dont remember where to find them anymore and dont want to give spoilers. Hmmm, you should have found at least one by now if you are in the strip.
How much is the speech check again?

Edit 2: I just checked, the speech checks 30 you wont even need all of the things i mentioned. Cut out Party time mentats. And maybe even the skill magazine.

Wow! This sounds like an uber quest in its self. I'll do it.

EDIT Speech check 30 and I'm on 14

If you are on 14, then buy the Naughty sleepwear, now you are on 24, and use a skill magazine.