How to keep cake topper from toppling over
You can make the base wider with white chocolate. No glue, and you can do it in advance so you don't need to have any electricity at the site.

Put a parchment paper round into an appropriately sized cake pan or a plate or shallow bowl. Stand the cake topper in the middle of the parchment paper. Carefully pour or pipe melted chocolate around the edge of the base and build it up, coating the base and widening it. Allow the chocolate to cool,  carefully peel away the parchment paper.

If the weather is likely to be warm, you may want to make the additional chocolate layer thicker so that it will not melt quickly and release the topper.

You could also widen the base with some other material (cardboard covered with foil, for example -- make a large cardboard disc, cut a hole in the middle for the stem of the topper, cut a slit on one side of the hole the size of the base, slide the base through and center it) and cover that with chocolate or frosting, but I think plain white chocolate would work well and it sounds like the bride wants to keep everything touching the cake edible (except the topper itself, of course).