Changing the look and feel of Dojo widgets is done using themes.
http://dojotoolkit.org/reference-guide/1.7/dijit/themes.html
You can see the themes that ship by default at
http://archive.dojotoolkit.org/nightly/dojotoolkit/dijit/themes/themeTester.html
(NOTE: This page is based on a nightly build, so soemtimes it is broken)
Themes are applied using CSS.
I'd create your own css style sheet.
Add the theme name to the body node.
<body class="tundra myTheme">
The particular css you are looking for is
.myTheme .dijitComboBox .dijitDownArrowButton {} /* The grey box */
.myTheme .dijitComboBox .dijitDownArrowButton .dijitArrowButtonInner { /* The arrow */
background: url(images/spriteArrows.png) no-repeat scroll 0 center;
}
/* Hover */
.myTheme .dijitComboBox .dijitDownArrowButtonHover {} /* The grey box */
.myTheme .dijitComboBox .dijitDownArrowButtonHover .dijitArrowButtonInner {} /* The arrow */
/* Active (mouse down) */
.myTheme .dijitComboBox .dijitDownArrowButtonActive {} /* The grey box */
.myTheme .dijitComboBox .dijitDownArrowButtonActive .dijitArrowButtonInner {} /* The arrow */
Using the developer tools with your browser will help you determine the css classes that you are looking to override.