G: TLDR: Yes in the broad sense, no in the fine print. Hedgehog quills and human fingernails are both keratin-based structures, but not the same keratin type, density, or micro-architecture. Functionally: same family of material; structurally: significantly different.

Direct answer

• Hedgehog quills are modified hairs. They’re built from α-keratin, heavily cross-linked, dense, and arranged around an air-filled core for stiffness and shock absorption.
• Human fingernails are flattened keratin plates, also made of α-keratin, but optimized for shearing resistance and compression rather than penetration or cushioning.
• So: same category of stuff, different recipe and different engineering.

Two quick grade-1 Japanese examples (kept simple):

1. はりの たんそざい（たんそざい）— The material of the quill
2. つめの かわ（かわ）— The shell of the nail

Bottom line

They share the same base protein family, but the structure, hardness, and mechanical purpose differ enough that they’re not “chemically equivalent” in any strict sense.

G: Short version:
You can paint a hedgehog quill with nail polish; the chemistry will “stick.”
You should not do it on a living hedgehog. The fumes and ingestion risk are bad for them.

Practical chemistry answer (still supporting the joke)

Nail polish adheres to keratin, full stop. Quills are keratin. So yes:
ポリッシュは つけられる（つけられる）— polish can be applied.

If you clipped a quill (naturally shed, not pulled) and treated it like a tiny rod of nail material, polish will dry normally and look normal. The porosity and curvature of a quill might actually make some colors pop because the surface is smoother than a fingernail’s plate grain.

The real-world animal safety note (brief)

On an actual hedgehog:

• The solvent fumes (ethyl acetate, butyl acetate, toluene substitutes) are dangerous in their concentration near a small animal.
• If the hedgehog licks the quills—common grooming behavior—it can ingest uncured polish.
• You’d also have to hold them awkwardly long enough for drying, which they will not appreciate.

If the joke involves aesthetics

Decorating shed quills works fine chemically and visually.
Decorating attached quills is a no-go unless the hedgehog has mysteriously signed a liability waiver and enjoys spa day.