I’ve never tried to fly with a shamisen, but often fly with a musical instrument. In the US, airlines are required to let you board with your musical instrument if there is space for it and it fits in an overhead bin or under a seat. In addition to checking with your airline, a couple of other things you can try are to choose a seat towards the back of the plane so you get to board earlier, before the overhead bins fill up. Also, with some airlines you can talk to the gate agent before boarding begins and explain that you have a musical instrument and ask very nicely if they would let you board with some of the pre-boarding people (like the ones with kids or who need extra help). All they can do is say no, and often they are fine with it. It will count as a piece of carry-on (unlike medical equipment), though, so keep that in mind if you’re not planning to check luggage.
Here’s a link to the federal regulation (middle column of second page states requirement): https://www.transportation.gov/sites/dot.gov/files/docs/Musical%20instruments_FR_final%20rule.pdf