Yes, there are many ways to wear the medallion. Beside the lanyard that comes free you can also get clips, watch attachments, necklaces, bracelets, silicone bands, etc. Of course all of those have some cost. If your wife likes to put it in her bra the clip might be the answer. Google search for Air Tag holders as those are the same size or Princess medallion holders.
https://www.amazon.com/dp/B07R93C77G?psc=1&ref=ppx_yo2ov_dt_b_product_details
https://www.amazon.com/OCEAN-Princess-Cruises-Medallion-Accessory/dp/B07V5KGFQR/ref=sr_1_3?crid=AHM86C5XUWPV&keywords=cruise%2Bmedallion%2Bholder&qid=1663704045&sprefix=cruise%2Bmedallion%2Bholder%2Caps%2C112&sr=8-3&th=1