This problem has a classical solution: Using and overriding the identity template is one of the most fundamental and powerful XSLT design patterns:
<xsl:stylesheet version="1.0"
xmlns:xsl="http://www.w3.org/1999/XSL/Transform">
<xsl:output omit-xml-declaration="yes" indent="yes"/>
<!-- -->
<xsl:param name="pNewType" select="'myNewType'"/>
<!-- -->
<xsl:template match="node()|@*">
<xsl:copy>
<xsl:apply-templates select="node()|@*"/>
</xsl:copy>
</xsl:template>
<!-- -->
<xsl:template match="property/@type">
<xsl:attribute name="type">
<xsl:value-of select="$pNewType"/>
</xsl:attribute>
</xsl:template>
</xsl:stylesheet>
When applied on this XML document:
<t>
<property>value1</property>
<property type="old">value2</property>
</t>
the wanted result is produced:
<t>
<property>value1</property>
<property type="myNewType">value2</property>
</t>