RGB is just a generic color mode. Photoshop always requires a specific color space, and sRGB IEC61966-2.1 is one. Others are Adobe RGB (1998) and ProPhoto RGB.
Your color settings aren't important. What matters is the profile embedded in the document. This will take priority and override the working space in Photoshop.
In the print dialog it should say sRGB IEC61966-2.1 under document profile, if that's the profile the document has. Under print profile, you go into the rolldown and pick the specific profile for your printer and paper type. These profiles are installed along with the printer driver - if the printer supports it.
If the printer does not support icc profiles, then you need to set "printer manages color" in the print dialog. The document profile will still read as sRGB IEC61966-2.1, but that's just for information. The profile is embedded in the file and you can't change that here.