Напиши 2 страницы.
Одной ставь display:none а другой block;
<table id="table" width="100%" cellspacing="0" cellpadding="0" border="0" style="display:block">
<tr>
<td rowspan="2">1</td>
<td>2</td>
<td>3</td>
<td rowspan="2">4</td>
<td rowspan="2">5</td>
</tr>
<tr>
<td width="19%">6</td>
<td width="41%">7</td>
</tr></table>
<div id="div" style="display:none">
<div>2</div>
<div>3</div>
<div>1</div>
<div>6</div>
<div>7</div>
<div>4</div>
<div>5</div>
</div>
Предлагаю тебе сделать одну кнопку под названием
<input value="Редизайн" type="button" id="button" onclick="reDesign();">
function reDesign(){
if (localStorage.getItem("design")==null || localStorage.getItem("design")==1){
localStorage.setItem("design", "2");
document.getElementById("table").style.display = "none";
document.getElementById("div").style.display = "block";
}
else{
localStorage.setItem("design", "1");
document.getElementById("table").style.display = "block";
document.getElementById("div").style.display = "none";
}