Depends on the "ick". Is it smell or someone poured maple syrup on it? Smell, you can try laying in the sun, spray with Febreeze (if you can handle that), place in plastic bag with newspaper for a couple of days. If it is "touch icky, is it centralized? Can you hand wash the one spot? Make sure you check the fabric and seams to make sure it is fix worthy, nor everything should be saved.
Most say to not wash a top-only because of raveling and wrinkling. You can cut the strings after (it's a pain) and iron (it's a pain) but it is doable. If it comes down to washing, the most gentle cycle your machine has. I have a hand-wash cycle, I can pretty much wash anything in that one.