The fluffy hair wants stripping out dont clip it
Easiest way is to use a fine comb with a handle such as a Spratts 73 using your thumb to help grip the coat as you use the comb to help ease the fluffy hair out. You can also use rubber thimbles to help grip the fluffy coat and again pull the coat a little to ease the fluffy coat out.
Grooming chalk can help rub a little into the fluffy hair then again using a comb or finger & thumb ease the coat out, i also find the fluffy hair combs out easier when the coat is wet i normally do it whilst i have conditioner in the coat before I rinse it out coat kings are good as well used when the coat is wet but a fine comb is good as well.
Hope that helps at worst i would thin but dont clip it .