Ok, the shoe-bax valentine is crumpled.
Why? Because typically anything made of paper or material (fabric, like for clothes) can be crumpled. Usually, things that can crumple, can also be shaped into a "ball" or other form. "His clothes lay crumpled in the corner."
If you get angry at your printer, you grab the paper and crumple it up into a ball and throw it on the floor angrily. The actual printer can crumple the paper. If you travel and packed your bag fast, you clothes might be crumpled when you open the suitcase.
Any sheet of paper or length of cloth (both substances that have flat soft surfaces) are said to crumple. Flowers [the petals] can also crumple or be crumpled when they dry. Each individual petal is somewhat soft and can dry up and become crumpled. Crumple implies a deliberate action by a human or a machine.
Crinkle has a similar semantic trait except that with crinkle there is the idea of sound. Tissue paper (that very fine paper that comes around a gift in a box) has a crinkly sound when you crumple it up. It can be crumpled up but also has the distinctive sound is crinkling. The same is true for silver-type or other satiny papers. Like the material used for keeping joggers warm after a race. When crumpled (creases are put into them), those warmers crinkle (make a particular type of sound which I simply do not know how to express better than this). Certain plastics also crinkle when you handle them. In short, for me, crinkle involves sound, crumple does not. Crinkling is like tinkling except it's for a material, not glass.
Crinkle cut chips for me comes from the world of fabrics. Crinkled fabrics are actually fabrics that have been crumpled but it's more marketing lingo to say crinkled because who wants to buy "wrinkled" fabrics? It also carries the hint of the sound while actually not making a sound. It sounds nice, like tinkley. (glass or metal tinkles when caused to make a sound a certain way).
Wrinkles are what every woman wants to avoid: both as lines on the face and in her clothes. Wrinkled clothing is not a great thing unless of course you are wearing them deliberately or because you do not care.
Normally, an old thing made of paper (a valentine) with creases in it would not be described as having wrinkles. Crumpled yes.