I really don't think you need a "lint-free" cloth to clean your heatsink, just make sure that what you use is clean and doesn't leave any lint. A diaper, cheese-cloth, or good quality tee-shirt type cotton is fine. Just blow off any lint with some clean air. A good example of non "lint-free" cloth would be kleenex.
Typically a "lint-free" cloth is a tack cloth used for refinishing wood or in automotive finishing because it doesn't leave lint behind that would spoil the finish.
Johnny