JSFiddle - React, Tailwind, and code Playground

HTML

<select id="dd" class="valueSkippedHyperSwap">
 
    <option value="^">None</option>
    <option value="1">One</option>
    <option value="2">Two</option>
    
</select>
<select id="dd3" class="valueSkippedHyperSwap">
 
    <option value="^">None</option>
    <option value="1">33 One</option>
    <option value="2">44Two</option>
    
</select>

JavaScript

$(function(){
   
$('.valueSkippedHyperSwap').change(function () {
       var item=$(this);
      if(item.val()!="^")
      {
        item.find("option[value='^']").remove();
      }
    });    
    
    
});