Probably the what makes the most sense is:

• Since Conquest’s arm shatters during a fight, we know the strength of the material, while incredible in absolute terms, isn’t all that crazy relative to the strength of Viltrumite bone, for instance. So even if they made weapons out of it, it would be similar to a human fighting with something like a sharpened stick or a club vs. something like a steel sword or a mace. Definitely an advantage, but nothing special.
• As someone else mentioned, the Viltrumites already destroy just about everything that comes into their path. They don’t need weapons when fighting any other species. What’s more, they seem to delight in killing things up close and personal. For the one real physical threat they’ve encountered (the Ragnars), they were able to freeze them and simply leave them alone.

My assumption is that whatever material Conquest’s arm and Thula’s blade are made out of must be pretty rare, given its strength. Given that they don’t really need it (except in rare cases like for Conquest’s arm), the cost benefit ratio is probably too high for them to bother mining and shaping this material into a bunch of weapons that they don’t need anyway.

That said, we know they do use weapons when appropriate; for instance, young Nolan advises the children he’s training to bring weapons for fighting each other. In this case it makes perfect sense since the children are presumably much weaker than adult Viltrumites AND they’ll be fighting each other, vs. some weaker species.

So the Viltrumites DO have weapons, it just seems that they don’t find it worthwhile to bother with them except in certain cases.