It does matter if you invoke your right to silence. First, if you do, that affects what police can do (they have to stop interrogating you). Second, it plays a role in "adoptive admissions". If the police are asking you questions (you are not under arrest) and they make some statement that implies that you committed a crime, your silence can be used against you: it can be taken to be a form of admitting that you committed the crime. The premise is that if they imply that you murdered X, such an accusation if false would be so outrageous to a reasonable, innocent person that they would protest, therefore your lack of protest (denial) is tantamount to a confession. However, you can protect yourself by preemptively invoking your right to silence. See Salinas v. Texas:
a witness who “ ‘desires the protection of the privilege . . . must
claim it’ ” at the time he relies on it...
the Fifth Amendment guarantees that no one may be“compelled in
any criminal case to be a witness against himself,” not an
unqualified “right to remain silent.”
Since any right can be waived, at any time, there is no magic expression that you can utter that nullifies a future waiver of a Constitutional right. The closest that you can come is asserting that you hereby exercise your right to an attorney and that you will not speak until you have consulted with your attorney (then you better shut up). Lawyering up only prevents them from further interrogating you. Don't hedge: say "I am asserting my right to silence and refuse to speak without a lawyer". "I think I should..." is not a definitive assertion of your rights.
If you are (briefly) stopped, police may ask if they can search you or your property. If they have a warrant or probable cause, there's really no point in saying anything. In the case that consent is required, you just have to remember to not consent, and it would not be a bad idea to explicitly deny consent. Each and every time they ask. The same with their statement "It would really help us if you would come to the station to answer a few questions". If you are under arrest, then you have to go with them: ask "Am I free to go?". You can say "I do not consent to any search".
Your proposed declaration of rights is pretty vague. Exactly what rights are you talking about? Your right to freedom of religion? Your right to bear arms? Your right to not have to quarter soldiers in your house? Your right to an education? Many detainee statements have been found by the courts to be ineffective because they were unclear. You could give it a shot and see if the Supreme Court accepts your "universal assertion of rights" as effectively invoking your specific 4th and 5th amendment rights. Unless you have something in mind (like, the 6th amendment), the most effective statement is a very specific one. Silence, lawyer, no search.