Hate to sweat? No problem. Work out, get your sweat on for a short amount of time, finish up, then shower, dry off, change clothes... Walla you are now sweat free and clean.
You like dry and crunchy things? I can think of a bunch of crunchy vegetables and fruit, although they have some water in them... I can't think of many dry crunchy and healthy things off the top of my head though... Maybe Granola, low on the sugar, or none at all?... My advice would be to try and expand your horizons. Try new food that have different textures with an open mind, but look for healthy dry and crunchy foods too. Actually, there are a lot of dehydrated fruits that are healthy, maybe you would like that? Maybe even add something crunchy in a not so crunchy meal so you feel more "at home".
Sports are not required to lose weight or be healthy. Ever try dance dance revolution? That's one of those interactive dance games I believe is on the WII, lots of overweight people have had huge success losing weight and getting in shape by using it.
If you have a schedule that allows you to stay up late, or wake up early you could go to a gym that is open 24 hours a day, late at night or very early in the morning when there are less people around. You may even get the whole area to yourself, who knows. Walking or running in the early morning outside may also be a good idea.
It sounds like you may need a big change in life to get in shape and be healthy. It absolutely can be done, but it will probably be quite a challenge.
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Don't you mind people grinnin' in your face