Can exercise help me manage my high cholesterol?

Very much so. There are couple of ways that exercise will help. Firstly, exercise stimulates the enzymes that help move LDL, that's the bad cholesterol, from the blood and blood vessel walls, to the liver. From there the cholesterol is converted into bile for digestion or excretion. So the more you exercise the more LDL your body expels.
Secondly through exercise you can reduce a type of fat called inter-abdominal adipose tissue or visceral fat which is fat in the stomach (not under the skin) and around the internal organs. This also helps to reduce cholesterol.

Eric is definitely right exercise has many beneficial effects on cholesterol particularly on LDL -c and abdominal fat.

Exercise is also very effective at improving the good cholesterol (HDL-cholesterol) and lowering your triglycerides (the fat in your blood).

Exercise also improves insulin resistance and helps improve the uptake of glucose from the blood and into your bod cells for energy, this can have a major effect on your cholesterol levels too.

Exercise also gives you more energy and releases endorphins that make you feel better and reduces your stress levels. High levels of stress can impact negatively on your cholesterol.

Many reasons to get out there and be active.

Aerobic activity is the best, initially lower to moderate intensity, and build up as you get fitter. Complete activities that you enjoy doing such as going swimming, walking and boxing or engaging in social sports, just to make sure that you enjoy exercising, so it's not boring.

Researchers aren't entirely sure how exercise lowers cholesterol, but they are beginning to have a clearer idea. One way exercise can help lower cholesterol is by helping you lose – or maintain – weight. Being overweight tends to increase the amount of low-density lipoprotein (LDL) in your blood, the kind of lipoprotein that's been linked to heart disease.
Part of the confusion about the effect of exercise on cholesterol stems from the fact that most early cholesterol studies focused on both exercise and dietary changes, making it hard to tease out which of these factors was actually making the difference. But recent studies have more carefully examined the effect of exercise alone, making it easier to evaluate the relationship between exercise and cholesterol.
Researchers now believe there are several mechanisms involved. First, exercise stimulates enzymes that help move LDL from the blood (and blood-vessel walls) to the liver. From there, the cholesterol is converted into bile (for digestion) or excreted. So the more you exercise, the more LDL your body expels.
Second, exercise increases the size of the protein particles that carry cholesterol through the blood. (The combination of protein particles and cholesterol are called “lipoproteins;” it's the LDLs that have been linked to heart disease). Some of those particles are small and dense; some are big and fluffy. The small, dense particles are more dangerous than the big, fluffy ones because the smaller ones can squeeze into the and set up shop there. But now it appears that exercise increases the size of the protein particles that carry both good and bad lipoproteins.“
Exactly how much exercise is needed to lower cholesterol has been a matter of some debate. In general, most public health organizations recommend, at a minimum, 30 minutes per day of moderate to vigorous exercise , such as walking, jogging, biking, or gardening.
But a 2002 study by researchers at Duke University Medical Center found that more intense exercise is actually better than moderate exercise for lowering cholesterol. In a study of overweight, sedentary people who did not change their diet, the researchers found that those who got moderate exercise did lower their LDL level somewhat. But the people who did more vigorous exercise lowered it even more.
The people who exercised vigorously also raised their levels of high-density lipoprotein (HDL) – the ”good" kind of lipoprotein that actually helps clear cholesterol from the blood. It requires a good amount of high intensity exercise to significantly change HDL. Even though moderate exercise was not as effective in reducing LDL or increasing HDL, it did keep cholesterol levels from rising.
Bottom line? Some exercise is better than none; more exercise is better than some.
Just how much of an effect exercise has on cholesterol is also a matter of debate. It has been found that the people who benefit the most are those who had the worst diet and exercise habits to begin with. Some of those people reduce their LDL by 10-15% and increase their HDL by 20%.