The act of asking for one gives you protections.
Likewise, the police may read you your Miranda rights and try to get you to sign something saying you know and understand them. You should refuse to sign, stating that you won't sign anything without a lawyer.
Signing it opens the door for further questions and a chance your answers can be used in court. Not signing it will generally lead to them skipping the questions, as there's little point.
[1] edit: to do this you refuse to give any name. DO NOT give a false name like "John Doe" - that's merely what they'll put on the paperwork if you refuse to give a name. Giving a false name is pretty much always a bad idea. Note that generally refusing to not give your name is probable cause for arrest in many jurisdictions and I believe may even be a misdemeanor in some places. I think it's generally only a reasonable route if the arrest was clearly illegal and disclosing your real name might make you a target for other reasons (e.g. immigration status). I do know someone who wasn't a citizen who was arrested while engaging in protected first amendment activities and refused to say a single syllable (lest their accent give away their status) and they were released as a john doe at their arraignment. But yes, YMMV.
1) Be polite. Always. 2) Make it clear that you're both two professionals trying to get through this as quickly as possible, both of you have better things to do. 3) If you must talk to someone, always talk to the person, never the hat.
Also, there have recently been court cases where someone accused of a crime didn't immediately VERBALLY exercise their right to remain silent, and that fact was used as evidence. Crazy stuff.
You should say essentially, "I chose to remain silent until I can speak to an attorney."