Very faint 1mm grey regular line growing along fingernail. 2 dermatologists (dermoscope) said its not melanoma. should i push 4 biopsy?

Let the Dermatologis: I think you have already engaged two dermatologists who agree that you do not have melanoma . I would trust them and keep an eye on your nail for any further growth or changes which might require a biopsy. The biopsy of the nail is cumbersome and only recommended if it is suspected melanoma, which will typically produce a vertical streak of black or brown pigment from base of the nail.

Watch & measure: Given the advice of 2 experienced physicians, i wild hold off for now and continue observation for now. If it should change at all, bring tis to the attention of your managing physicians -give it 2-3 months.