From ShaveWiki
Flights Originating in the United States
Per current TSA guidelines you may carry a safety razor within your carry on baggage. However, it cannot have a blade within the razor and all razor blades must be in your checked baggage or purchased at your destination. Blades for cartridge razors (Mach 3, Fusion, etc) are allowed with no restrictions.
In addition to restrictions on blades in carry on luggage you'll also want to place any gels or liquids in < 3 oz containers and place all the containers in a quart sized zip-top plastic bag. Examples of liquids and gels used in shaving include but are not limited to: shaving creams, after shaves, colognes, pre/post oils, etc.
International Flights
Same restrictions on razor blades within carry on luggage as above.
In addition to restrictions on blades in carry on luggage you'll also want to place any gels or liquids in < 100 ml containers and place all the containers in a zip-top plastic bag which length + width dimensions are < 40 cm. Examples of liquids and gels used in shaving include but are not limited to: shaving creams, after shaves, colognes, pre/post oils, etc. Note the container must be 100 ml or less and not just the actual amount of product left. For instance, if you have a half full 200 ml tube of shaving cream this will not be allowed in your carry on luggage.