What is the button doing?  If it's calling a client JS function, then you could use SSJS to emit JS code to call it when the page reloads.

Here is a bit of code I use to call a clientside function using the ids calculated serverside.

Note how the input field is set escape=false to allow me to emit html into the page.

 

<script language="Javascript">
                                    XSP.addOnLoad(function () {
                                    initLocal();
                                    }
                                    );
</script>
                              <xp:text escape="false" id="elementidfield1">
                                    <xp:this.value><![CDATA[#{javascript:var out="<script language=\"Javascript\">\n";
out += "var charTextId = \"" + getClientId("charTextId") + "\";\n";
out += "var divCWidthId = \"" + getClientId("EntryDisplay") + "\";\n";
out += "function initLocal(){\n";
out += "var charElem = document.getElementById(charTextId);\n";
out += "var divCWidth = document.getElementById(divCWidthId);\n";
out += "charElem.style.fontSize = pointSizeToFit(charElem,divCWidth.offsetWidth);\n";
out += "}\n";
out += "</script>";
out}]]></xp:this.value>
                                </xp:text>