I like to play straighter too, but have found sweeping to be really effective to stop the bowler getting on top. Although I'm not good enough to do it for every ball on off or middle, it's worked well for me for anything on leg or going down.
But what gave me the confidence to do it more was an entire net session last winter on nothing but sweeps and reverse sweeps. We rotated around different nets, practising different aspects. Sometimes throw downs, sometimes bowling machine, sometimes just bowlers. The best for me was the one just doing reverse sweeps - I'm old enough to remember when this shot was guaranteed to get you nothing but abuse from your own team mates, let alone the opposition! But now it's a really effective and common shot, and watching the juniors that have grown up with it (and a lot of other shots I don't have) is just great. I got pretty good by the end of the session, but still can't bring myself to use it in a game.
The only downside of that session was that 2 solid hours of basically doing squats meant that I couldn't move for a few days afterwards!
And totally agree with getting your bat up high first, for both types of sweep. Coming down onto the ball reduces the risk for me.