This is how I do it. Get a lightweight gun such as a NAA .22 magnum, Ruger LCR or S&W 442 or 340 PD and carry it in an ankle holster fixed to your arm. Velcro ankle holsters work just as well around your weak side bicep and you can crossdraw. Wear a T-shirt with sleeves long enough to keep the gun concealed. These guns are not expensive (except for the 340) but they are reliable. Since you will be sweating, rust will be an issue even with a stainless gun so wipe it down with a good gun oil before placing in the holster and again when you get back home. Even if the gun does rust away and you have to replace it every few years, it's still a good bargain.
I don't like fanny packs because people know that's where your money, house key and gun are located. Just keep everything light and put it in a pocket or attach it to your body.
Example:
http://www.naaminis.com/mag_hol.html