You can use a switcher to waste the effluent in the first few minutes and then to connect to the mass spec. EDTA is not helpful in your case. Salt remover device before injector is also an option, if you have one.
Depending on the size of your peptides, you could also do some ultrafiltration by using a low enough cut-off membrane. Nowadays you can find filters which you can put into tubes and centrifuge them which simplifies and speeds up the process.