Short answer: yes. Long answer: the thing wrecking your pattern is not the hat, it is what is inside it.
Most people who put real work into their waves end up avoiding caps entirely, or accepting that they will have to brush the pattern back every time they take one off. Neither is necessary. But it is worth understanding what is actually going wrong, because the fix is specific.
The four things a cap does to waves
It presses a dent. A crown that sits too tight, or an unstructured cap that collapses onto your head, puts a hard line across the pattern. The tighter and the softer the cap, the worse it is.
It snags. The inside of almost every cap is cotton, poly twill or a mesh sweatband. All three have surface texture. Hair moving against texture catches, and eight hours of catching is what you are seeing when the pattern looks fuzzy instead of sharp.
It compresses too hard. Over-tightening does not lay the pattern the way a durag does. It just gives you a headache and leaves a mark on your forehead.
It traps sweat. Moisture builds under the band, and a wet pattern lifts. Cotton sweatbands make this worse because they hold the sweat right against your hairline.
What actually fixes it
Structure in the crown. A six-panel structured cap holds its own shape. That is the difference between a cap resting on your head and a cap pressing into it. Unstructured dad hats are the worst offenders here.
A smooth lining. This is the big one. Satin has almost no surface texture, so hair slides across it rather than catching. It is the exact same principle as a durag or a satin pillowcase — the material has just never been put inside a cap you would wear out.
A strap, not a snapback. Snapback teeth adjust in fixed jumps, so you end up choosing between slightly too tight and slightly too loose. A strapback with a metal slide adjusts continuously.
Mid-depth, not shallow. A shallow crown sits down on the pattern. Mid-depth sits above the ears with room underneath.
What about a wave cap under a hat?
It works. It is also two layers, it is hot, and it usually shows at the back. Fine for a quick errand. By hour six on a warm day you will be over it.
A satin-lined cap does the same job in one layer, with nothing showing.
Straight from the chair
The 48 hours after a fresh cut decide the next two weeks. That is when a cap is doing the most damage, and also when most people wear one, because a fresh line is exactly when you want your head covered.
If you are going to wear a hat over a fresh cut, wear one with satin against it.
Where we come in
Every Cappin' cap is lined edge to edge in red satin — all six panels plus the sweatband, not a patch at the band. Six-panel structured crown, pre-curved visor, adjustable strapback 21–24 inches. One size, $34, designed in Los Angeles.