Are your friends at least fun guys to hang out with?
If so, go out with them anyways!
Yah, they might rib you a bit if they think approaching women intentionally is awkward. Don't take it too seriously, man - guys friends rib each other, that's just what they do. Some probably do think it's strange and juvenile, but chances are some of them wish they had the balls to do it too and are just looking for an easy out. The pressure might even force you to get a hold of your nerves faster.
And if they see you start to get real results, I'll bet money they change their tune...
If you really don't know guys that like to go out and have a bit of fun, whether to chase skirt, shoot pool, or have a drink or whatever, maybe it's time to meet some. Female friends are great for this too - girls I hang out with as friends love to go grab a random happy hour appetizer and drink as long as their schedule is open. Being out socializing with girls is great practice for you, and if they're cool, they'll help you try to meet other girls.
Just don't be the guy who's paying for it all if she's just a friend, or following her around like a lost puppy trying to get in her pants. That's not going to make a good wing out of her.
One thing I noticed about your post - you don't mention any of the great things about going out, so it's no wonder you have to make such a conscious effort to do it. My advice: Start learning to appreciate the experience of being out at restaurants and bars.
I have my introverted moments where I like to chill home and read, and I work online at home, but almost every day I just have to get out for a little bit or I start feeling a bit boxed in. My girlfriend is a bit of a homebody and could sit home all week if I let her, but once I get her out she always has more fun.
I grew up working in restaurants and bars, so I guess I just really learned to love whole lifestyle and culture of dining establishments. The ambiance. The music. Laughing and meeting new people and making memories. The people who make it a career are often very fun-loving people to be around (get to know them and they'll show you the best-kept secrets in town). A good wine. A good scotch, gin and tonic, or more creative cocktail. Well-prepared, delicious food. And the experience of being catered to and waited on.
Become a man of great taste.
My point is, yes, go out to approach women if you need practice, but also keep in mind that it's so much easier to get people (men and women) to love being around you if you learn to actually love life. And that includes going out.
Get online and make a comprehensive list of all the cool happy hour specials going on around your city. Try developing an interest in mixology, wines, craft beers, or dining (doesn't have to be fine dining or always a good meal). If you just don't see the point of spending time or money on these things, you probably just don't know enough about them - most things in life are so much more fascinating than you might think at first glance once you dig in deeper.
Reading an interesting book about food or mixology, history of alcohol, etc, could be a way of drawing out some of these tangents. I read a book called "Acquired Tastes" a long time ago that might be a good start for you.
Other options would be learning more about coffee or playing pool. If you don't want to spend your time only in restaurants and bars - develop other hobbies and interests that lead to social interaction (i.e. hanging out at the rock climbing gym).
Then when you go out you've got a way to make it more interesting (for yourself and others) - because you actually appreciate (and know about) everything more than your average joe. The more you're out, what do you know, the more you'll bump into girls. Look at them, make eye contact, flirt, approach. Not so complicated when you put it that way, right?
Savor the experiences of life more AND increase your approaches both at once.
Hard to lose with that attitude no matter what game you're playing.
