In most jurisdictions you can refuse to
testify against yourself but you are still required to give up all physical evidence against yourself if an appropriate warrant requests them, the immunity only applies to things in your mind.
Things like hiding or destroying evidence of a crime generally are separate crimes of which you can be convicted even if you're acquitted of the original crime (e.g. burying a corpse in the woods or throwing a gun in the river).
Destruction of evidence with the intent to hide it from prosecution also may enable so called 'adverse inference' where essentially the jury/judge can assume that the destroyed evidence actually showed what the prosecution intended to find there. For example, if you're being prosecuted for possession of child sexual abuse material, there's a warrant for your hard drive, but it gets fully destroyed because you have rigged some device to destroy it (and the prosecution proves that you did that with the intent to destroy evidence) then the court may take it as a fact that the hard drive did indeed contain CSAM and treat it as sufficient evidence to convict you.
In short, self-hosted service on a rented service does not provide much protection.