You don't need to removed your back brake just because you're riding with a fixed wheel, it's generally normal to have a front brake on a fixed wheel bicycle because under the UK law, the fixed wheel tranmission counted as a brake (although it's recommended to have foot retention), but it's not a necessity to only have a front hand-operated brake.
Choose what make you feel comfortable, not accordingly to the general view of how a fixed wheel bicycle should be.
You don't need to removed your back brake just because you're riding with a fixed wheel, it's generally normal to have a front brake on a fixed wheel bicycle because under the UK law, the fixed wheel tranmission counted as a brake (although it's recommended to have foot retention), but it's not a necessity to only have a front hand-operated brake.
Choose what make you feel comfortable, not accordingly to the general view of how a fixed wheel bicycle should be.