This question asks about the feasibility of an Orion-like pulse propulsion system using chemical explosives instead of nuclear explosives as pulse unit. Unfortunately, those simply lack the energy required to make it worthwhile. If we are going to lug all those chemicals for their energy, we are better off using said chemical energy with conventional rockets in the first place.
(There is one science-fiction novel I won't name to avoid spoilers, where the protagonists end up using this method. But they have to build a spacecraft - any spacecraft - from scratch on a deadline, in which case desperate measures make sense)
But who said that we had to lug them on board the craft in the first place?
Chemical explosive pulse units exist in self-contained packets, and those have been routinely projected at considerable distances, sometimes hundreds of kilometres. Those are called artillery shells. They even come up with terminal guidance systems of remarkable precision.
So, similarly to how a ground laser can propel a laser sail or a laser air-breathing craft, howitzers could propel a spacecraft with an Orion-like pusher plate by firing shells at it, programmed to detonate right below the plate. This would specifically be to accelerate a craft in atmosphere, where air makes detonations transmitting considerably more energy - which is why the atmospheric pulse units for Orion would have been much, much less powerful than the space pulse units - merely the equivalent of 100 tons of TNT.
Has any such system been studied or proposed? Would thermobaric explosives help? Apart from little details like security, impossibility to throttle, common sense or the use of heavy, long-range military weapons, are there drawbacks that make this system infeasible?