Here is one way to handle this:
It may even be sufficient to add a parameter to the DVIOnePageApplet, called showControls. If the parameter is set to false, then never show the controls window.
One possibility is to take as input both a dvi file and an html file, and replace each occurrence of the string $equation with an applet which will display the next equation from the file.
It may be reasonable to require that every equation is on its own page. This makes it easy to compute bounding boxes for the equations, and allows the most re-use of existing code.
A shell script or html parser could extract the TeX parts, run them together into a single tex input file, use TeX to produce a dvi file, and then use the modified DVISplitApplication to replace the original TeX source text with applet references.