Just a few misconceptions.
It's not going to cruise at M10, it's got to reach M10
Could be an hour+, could be a minute+, could be 5secs. It's all good (although they may think 1 hr at M10 is better I think that claim is likely to trigger the BS detector big time).
With that spec there's lots of room for "creative engineering interpretation."
"Cheating" is for exams IRL if it gets the job done, it gets the job done. End of.
That said anyone talking SCRamjets is also talking stupid money.
OTOH the USAFRL got a plane in the air with an actual meatsack at the controls on a Pulse Detonation Engine in 2006. Only something like M0.8-1.2 but it was v 0.8 tech at best and they are sure they could do much better.
Incidentally that M10 is not even clear if it's M10 horizontal (leaving the other M13 to the 2nd stage) or vertical (a whole different ball game).
BTW This project is being headed by Jeff Sponable, who ran the SDIO DC-X programme that built a VTOL M3 demonstrator for about $60m in the early 90's. The RFI talks about an "aircraft" but later in it says "aircraft like," which is also a whole different game.
Trouble is until the "contractor open day" there's a lot that's up in the air (pun intended). 1000-4000lb fair enough but what's the shape? Form factor? Payload density? That will make a huge difference to what could work for this.
I'd (more or less) agree with Trevor-Potts comment about this. Conceptually a simple nuke is fairly simple to construct. The AEC hired 3 Physics PhD candidates in the late 60's to try to design one given what was available in the open literature and could be purchased from the USG Printing Office. Their report is (AFAIK) still classified.
I'll suggest that what needed 3 PhD;s 4 decades ago has come considerably down the food chain, although I'm not quite ready to say "Nuclear terrorism for skiddies" yet.
No I can't do it. I do not hold a security classification with any organization. I'd suggest a key feature is how enriched the U235 has to be to get a fair chance of a bang. Historically that's meant to have been about 70%+ HEU, but AFAIK some have been done in the LEU range (4-20%). As water cooled reactors don't work without enriched Uranium (except the original CANDU design, which sidesteps the whole enrichment problem) that means probably 80-90%+ of the worlds reactors could source the core raw material for some unpleasantness, which implies 80-90% of the countries that have reactors could source a device of varying levels of sophistication.
OTOH damm few countries have built aircraft to exceed M3. IIRC the US, USSR and (I think) France and that's it. The UK would probably be in there if was not for that rampant todger bandit Duncan Sandys, but we've all passed a lot of water since those days. :(
OTOH 2 consider how many countries have achieved orbital launch where the LV routinely stages at M10.
VTO is relatively easy.