Playing close to the channel is the same as hitting a golf ball over water. The fear is psychosomatic. Shooting 10 pins for right handers and vice versus for lefties probably falls into the same category.
What a bowler can and can't do is mostly in their heads. Newbies who spray the ball all over because they haven't gained the necessary control have a right to be afraid, but anyone who's been shooting for a few months should understand that they can throw their normal shot wherever they choose.
Whether that shot is down and in or cross alley or from deep inside, the basic shot shouldn't change. Failure to learn this simple lesson early can turn a person into a fundamentally flawed bowler for years to come
Practice/experience will make the fear go away.
The more angles a player can shoot from, the more advantage that bowler will have over those who cannot or will not. Nothing drives
me crazier than bowlers who say they can't do something or won't even try it. They become like 4 year olds at dinner. Knowing how their ball will react from the different angles may require some trial and error, but their delivery shouldn't change.
There's nothing more entertaining than a person who otherwise is a good bowler, looking like a giraffe at a watering hole trying to shoot anything but the 2nd arrow.
Now that I've ranted, here's a few thing to help with shooting down and in.
Unless the lanes are like ice, don't use your strongest equipment. All delivery errors will be magnified by an aggressive ball.
Watch axis rotation for 2 reasons; First if you pull a ball with too much axis rotation off the corner, you can wave bye bye to the head pin. Secondly, depending on how close you are to the channel, the simple act of going inside out with your hand can airmail a shot into the channel.
Don't move so far right that you have to increase speed to hold the ball off the nose. Failure to hold that speed will give the same result as too much axis rotation.
Don't expect the corner to last very long. If the lane oil is crowned from a THS, the area right of the 5 board will be driest. The one and 2 boards may be like the rail on a pool table. If your ball get to them early, the result will be on the nose or left.
Be as smooth as possible and get the ball off your hand as clean as possible. Any loss of body angle, pulling the ball instead of waiting, letting your elbow getaway or going over the top of your shot will be much more disastrous off the corner.