Just out of curiosity, I did a quick search online to see where there are museums of shaving or barber shop items. Here is a list of some I found. It is not exhaustive and probably not complete, but it's a starting point.
National Barber Museum
Winchester, OH
Open by appointment only
https://www.nationalbarbermuseum.org/
New York City Barber Shop Museum (and operating barber shop)
New York, NY
Appointments
https://www.nycbarbershopmuseum.com/
National Museum of American History (Smithsonian)
Hair Removal section in the Medicine & Science Collections
D.C.
Time-entry passes
https://www.si.edu/spotlight/health-hygi...ir-removal
Shaving artworks
Philadelphia Museum of Art
Philadelphia, PA
Open
https://philamuseum.org/search?q=shaving...=0&size=12
History of the Barber Profession exhibit
Johnson County Historical Society Museum
Coralville, IA
Currently closed
https://johnsoncountyhistory.org/museum/
1930s Barber Shop
The Bundy Museum of History & Art
Binghamton, NY
Open
https://www.bundymuseum.org/exhibits/1930s-barbershop
Shaving Collection
National Science & Media Museum
London, UK
Open by pre-booking
https://collection.sciencemuseumgroup.or...-(shaving)
Mühle Museum
Mühle London Barbershop
London, UK
Open
https://www.muehle-shaving.co.uk/blog/ta...hle-museum
Giovanni Lorenzi Collection
G. Lorenzi - 1929 Coltellinaio
Milan, Italy
Appointments, apparently
https://www.fondazionecologni.it/en/inte...ni-lorenzi
Feather Museum of Razors
Seki, Gifu, Japan
Open
https://www.feather-museum.com/about.html
National Barber Museum
Winchester, OH
Open by appointment only
https://www.nationalbarbermuseum.org/
New York City Barber Shop Museum (and operating barber shop)
New York, NY
Appointments
https://www.nycbarbershopmuseum.com/
National Museum of American History (Smithsonian)
Hair Removal section in the Medicine & Science Collections
D.C.
Time-entry passes
https://www.si.edu/spotlight/health-hygi...ir-removal
Shaving artworks
Philadelphia Museum of Art
Philadelphia, PA
Open
https://philamuseum.org/search?q=shaving...=0&size=12
History of the Barber Profession exhibit
Johnson County Historical Society Museum
Coralville, IA
Currently closed
https://johnsoncountyhistory.org/museum/
1930s Barber Shop
The Bundy Museum of History & Art
Binghamton, NY
Open
https://www.bundymuseum.org/exhibits/1930s-barbershop
Shaving Collection
National Science & Media Museum
London, UK
Open by pre-booking
https://collection.sciencemuseumgroup.or...-(shaving)
Mühle Museum
Mühle London Barbershop
London, UK
Open
https://www.muehle-shaving.co.uk/blog/ta...hle-museum
Giovanni Lorenzi Collection
G. Lorenzi - 1929 Coltellinaio
Milan, Italy
Appointments, apparently
https://www.fondazionecologni.it/en/inte...ni-lorenzi
Feather Museum of Razors
Seki, Gifu, Japan
Open
https://www.feather-museum.com/about.html
John