So, I am normally terrified with social anxiety during social events. I almost never socialize without it because I get panicky and overwhelmed. I have told my DR this and he prescribed me SSRIs and a benzo, but they don’t help much. What to replace booze with? What skills can I learn? I have a first date coming up and I don’t want to have to drink during it? Or should I put the date on hold till I feel more comfortable in my soberity?
I would just tell the other person you are sober so they know that you won’t be drinking. That way that worry is out the window of “what they will think”. 

Maybe try some CBD oils. I know some bars have CBD seltzers too!
Agree with Brady. If the date is worth it, that shouldn’t matter and who knows, your date might be sober too and regardless, by the response, it will give you a better idea whether you should go.
Nailed it!
What is the plan for the date? Maybe schedule a day thing so you could go out for smoothies or a walk? Or some activity where you won't end up at a bar or restaurant where there's lots of drinking around you. I always liked going for a walk to help with first-date nervousness. Hope you have fun!
I agree with Laura 
be careful with the benzos!! I take a small dose (25mg) of Seroquel (4 times a day) for my anxiety and i don’t feel like a zombie like benzos do. Also benzos can mess with your memory. Seroquel is a mood stabilizer and I find it totally gets the anxiety and stomachs in a knot to go away. I used to think I had terrible stomach problems until I took seroquel and realized it was my anxiety cause my stomach pain. It’s not as strong as benzos too. I literally used to have panic attacks all the time and you could tell i was always on edge. That’s what helped for me take what you need from that.
Plus the person your going on a date with is probably just as nervous! And people think about themselves first they are gonna be wondering if you can tell how anxious they are. Just laugh it off and try to let go and worse thing just fake it till you make it !!
I second the q.i.d. Seroquel 