A wound made by a bladed weapon would have drawn attention
You all right? If they find a body with a stab wound, the whole city
will be looking for us.
Assuming that bloodshed is prohibited in Vaes Dothrak, getting into a fistfight and killing someone may be technically disallowed, but it is something a sufficiently foolish or drunk resident may do. Killing someone with a blade, given that weapons are prohibited within the city? Clearly the work of a foreigner, and thus of high priority.
A death via blunt force trauma will undoubtedly be looked into, but perhaps not with the same urgency. Thus the need to conceal the cause of death.
The rules against bloodshed may not be so hard-and-fast
In the novels, it is established that any sort of bloodshed (of humans, at least) is prohibited, along with bladed steel weapons.
Many of the men were drunk on clotted mare's milk, yet Daenerys knew no
arakhs would clash tonight, not here in the sacred city, where blades and bloodshed were forbidden.
—A Game of Thrones
On the TV show, people generally speak of the ban on weapons when they mention Vaes Dothrak:
JORAH MORMONT: Don't let them see you carrying a sword in Vaes
Dothrak. You know the law.
VISERYS TARGARYEN: (sheaths his sword) It's
not my law.(turns and puts another egg in the bag)
and
It's forbidden to carry weapons in the sacred city.
and
You all right? If they find a body with a stab wound, the whole city
will be looking for us.
On the other hand, Viserys Targaryen does not (though admittedly he is an individual with perhaps not a stellar understanding of Dothraki culture, as evidenced by his final fate):
VISERYS TARGARYEN: They can't kill us. (pointing his sword again at
Jorah) (Drogo mutters to his Dothraki soldier, who then gets up) They
can't shed blood in their sacred city.
Indeed, the translation of the Dothraki dialogue from the episode makes the reasoning clear:
FORZHO : It is forbidden to spill blood in the sacred city.
MORO: It is forbidden to carry weapons in the sacred city.
FORZHO: So we don’t spill blood!
MORO: Well… There’s always a little blood.
FORZHO: Not when you strangle them.
It seems that not all the Dothraki practice the prohibition on spilling blood so firmly, and that bloodshed through non-weapon means is not unheard of (not surprising, given how many Dothraki fetishize violence elsewhere).
So while avoiding spilling blood may be the point of the prohibition on weapons, some Dothraki seem to interpret the prohibition rather literally. Of course, this still probably wouldn't let someone get away with the murder of a prominent individual, but as mentioned previously, it would make the death much less suspicious.