> "try to make it a clean fusion design" would actually be enough here
Most of fallout in a "regular" nuclear weapon comes from uranium fission by products and from neutrons activating the surrounding materials. In addition, most thermonuclear (fusion) bombs use natural uranium tamper to contain the fusing hydrogen. This tamper soaks up fusion neutrons and fissions, and that actually produces a significant part of the overall yield.
But that's not the only option. It's possible to use a lead tamper instead, so it won't produce any fission byproducts. The Soviet Tsar Bomba did that, and it resulted in the cleanest nuclear explosion on a per-kiloton-basis.
It's also possible to add a boron neutron absorber around the fusion stage to further limit the amount of fusion neutrons that can create dangerous activated materials.
Of course, even a relatively clean weapon is still going to produce plenty of pollution.