You don't need guns. I'll be the first to admit that they can become a crutch. You just need to fight in a different manner. And it is a fight, whether for survival or straight up battle.
My plan was to stockpile and hang in my attic for a few week so I could figure out what kind of zombies are out there. Hopefully most of the zombies will be gone and I won't have to fight very many. Then try to go to Alaska or northern Canada.
First thing to remember about a pandemic, and lets face it. If a zpoc ever happened thats exactly what it would be is a pandemic. Pandemics typically last for 6 months before the spread of a virus slows down. Honestly your not going to be able to stay in your attic that long. Your best chance is to get out, and get out fast.
My best recommendation to you is this. Start buying some survival books, especially ones that explain how to survive in the elements. There are good one out there that will show you how to build shelters in the trees. You have to worry about critters that have been eating man for many years, and zeds too.
I would get as much survival gear together as possible, possible find a place or two in the woods out of away from people that you can stash some supplies. I would look at MRE's. They come in mylar bags that don't degrade very fast. You could stash them for years if buried in a container that would keep water out. Their also high in calorie, so you can limit your intake to one a day, and spread them out farther. The human body only requires 1200 calories a day, so 5 pounds a week is exceptable weight loss until it levels out.
I would also recommend becoming familiar with several firearms. I understand what you said in the beginning, but if your on the move and zpoc hits your eventually going to come across a firearm somewhere. You'll be scouting a gas station or a small store looking for can food, and will run across a dead police officer with his service pistol still on him. Or a small revolver left in someones cash office for a small business. So its always a good idea to learn how to operate a firearm.
Oh and some other quick things I just thought about. Look for revolvers if possible, there about as simple and no nonsense handgun you can get. On most models the cylinder release is on the left side of the firearm. This will release the cylinder and allow you to check if the pistol is clear, and reload it. Aiming a pistol isnt as hard as it sounds. Line the front dot up with the target, line it up between the two back dots, squeeze slowly, follow through. Sounds simple, but it takes practice.
Another good thing to do is find several automotive manuals for very common cars, perferrable diesels. Then learn how to hot wire them. Its fairly simple, you can watch countless videos on youtube about how to do it. As well as making biofuel with nothing more than chemicals you can scavenge in a hardware store, and a metal gas can. I know it sounds like a lot of work, but chances are it could keep you going.