There is no honest answer to that without knowing a lot more about the specifics, and anyone who tells you otherwise is guessing.
A 10-year-old simple assault warrant is a misdemeanor, which is on the lower end of the spectrum. That works in your favor. But the outcome of turning yourself in depends on several things that vary case by case: the jurisdiction, the judge, the original circumstances of the assault, whether the victim is still involved or has any interest in pursuing it, and most importantly your criminal history since the warrant was issued. If you have stayed clean for a decade, that carries weight. If there have been other incidents, it complicates things.
The smartest move here is to hire a criminal defense attorney before you do anything. A good lawyer can pull the case details, contact the court, and in many misdemeanor situations negotiate a resolution before you ever set foot in a courtroom. They may be able to get the warrant recalled or arrange a surrender on terms that minimize or eliminate jail time entirely. Walking in cold without representation is the riskiest version of this.
Ten years is a long time to carry something like this. Whatever the resolution looks like, getting it handled means you stop looking over your shoulder. That alone is worth the effort of making the call to an attorney.
If you want to get a clearer picture of what is actually on your record before taking next steps, TruthFinder can pull that information quickly and give you and your attorney something concrete to work with.