Also see HTML text input allow only numeric input.

Add a test to check if it's the first character and allow "-". Otherwise, run the other tests. e.g.

function allowNumbersOnly(e) {
  let len = e.target.value.length;
  var code = (e.which) ? e.which : e.keyCode;
  if (len == 0 && code == 45)  {
    return;
  }
  if (code > 31 && (code < 48 || code > 57)) {
    e.preventDefault();
  } else if (code == 109) {
    e.preventDefault();
  }  
}

window.onload = function() {
  document.querySelector('#i0').addEventListener('keypress', allowNumbersOnly, false);
}

<input id="i0">

However, that only allows entry of "-" as the first and only character, it can't be added later to change say "1" to "-1".

Personally, I find this kind of UI feature very annoying, e.g. it prevents keystrokes to copy and paste values. Just let the user enter whatever they like and deal with it. If it doesn't fit the required criteria, just let the user know with a friendly message and let them fix it.