Importing shells from a US beach into Japan

The official Japan Customs Procedures of Passenger Clearance page omits any mention of seashells or shellfish. They fall under no category of Prohibited Articles, and under Restricted Articles, while it says

Plants and animals must be presented to the plant or animal quarantine officer for quarantine inspection prior to Customs examination.

the shells themselves are neither plants nor animals, and more akin to bone or fur (I would expect that you would have boiled or otherwise sterilized them before packing, to ensure that anything organic left inside doesn't smell).

The same language is provided in the official Customs Guide for Visitors, which also omits any mention of shells or shellfish.

The IATA Travel Centre Japan page is another reliable reference (though some of the wording is confusing), and the only additional information it provides concerns import duty; you are exempt from customs charges on the first JPY 200,000 of personal effects (what the sand dollars would be considered if you have them as a personal keepsake or for a personal gift).

The main reasons countries impose customs restrictions are to protect domestic revenue, protect domestic industry, protect the domestic environment, and to protect domestic public health and morality. Since there seems to be no agricultural or health restriction on marine life, it doesn't seem like Japan would consider a sand dollar to be a threat to any of those things.