No, don't throw your scales away. They show any day-to-day gains or losses when riding multiday tours and expeditions.
The beauty of skinfold calipers is they tell you your fat % regardless of how muscular you are.
I am 5'9", 13 1/2 stone and 17 % fat +/- 0.25 %. That's pretty damned good for a 50 year old.
As has been said on another thread about weight loss, there comes a time in a cyclist's life when the leg fit of a pair of trousers becomes tight for the desired waistband.
You and I, cyclists, are not the average person; not even the average athlete. We develop our bums and leg muscles to a greater extent than runners or swimmers.
The BMI charts and on-line weight management sites DO NOT apply to us.
I have skinfold calipers. I also have Bioimpedence scales, but the readout from these is grossly effected by hydration levels, and a consistant, repeatable result cannot be obtained if I am cycling various distances and durations.
Don't bother with Bioimpedence scales.
After a while and some experience, a simple pinch of the suprailiac fold will give you an idea of where you are.
Remember the old "pinch more than an inch" Kellogs catchphrase?
That's all there is to it.