As jcjh20 said, it depends on where you live and what part of the beach you like. IMO the drive through Ft Myers Beach would take longer than getting there! It's a parking lot during certain periods, especially in Feb during Spring Break.
The Cape is vast, but using Cape Coral Parkway and Skyline as a starting point, you should be on Estero Boulevard, one of the main roads on Ft Myers Beach, in less than 30 minutes unless you leave during a very busy time of day.
Another suggestion might be the beaches on Sanibel. I haven't lived on Sanibel in many years and I know the bridge is expensive, but I used to have a sticker from Lee County and I drove to Cape Coral all the time. You might want to check into that as an option. The beaches on Sanibel are beautiful and the areas closer to the bridge aren't very far at all from the Southeast Cape..maybe 30-35 minutes.
I live in Bonita Springs near Barefoot Beach and have a doctor on Del Prado near the Coralwood Shopping Center. It takes me about 45 minutes to drive there. I take route 41 to Fort Myers and go over the Cape Coral bridge at College Parkway and turn right onto Del Prado. I can also take Colonial/Veteran's (midpoint bridge) and it's about the same.
One thing to consider is how often you will be going to the beach. What's an extra 15 minutes if you are only going to drive to the beach once or twice a month? Most people who move here think that once they live in FL they'll spend 1/2 their lives on the beach, but after a year or 2 they forget it's there. I guess it depends on your lifestyle. What I like about living in Bonita Springs is that, in the summer, I can still spend a couple of hours at the beach after working all day. However, I can't afford to buy a house here so I'm also looking for a home on Cape Coral. BTW, I stopped taking those long walks and rarely go to the beach any more.
Good luck! (yes, most of Cape Coral is safer than Fort Myers, although crime is on the rise everywhere)