If you are embarking near a tower, you only have to worry about what the necromancer can see and animate. If you are in an animating biome, there are many things that become very dangerous when they die.
The greatest risk to dwarfs fighting hand-to-hand with common undead (animated by necromancer or biome) is that dwarfs suffer from exertion and pain and that undead do not.
Do not get too hung up on the value of silver maces verse steel axes. Neither will help if the undead is big. A water buffalo is about 16 times the size of a dwarf. If a necromancer's army kills your water buffalo and animates it, you have a problem that maces and axes will not solve.
Your dwarfs will engage and they will be doing well, swinging and chipping bones, bruising muscle, and denting things. They will be blocking shots with shields and dodging. Then they will start getting tired and the undead will score a hit, the dwarf falls over as something explodes in gore, that dwarf dies, and the other dwarfs are still just chipping bones, but they are starting to get tired. No matter what people say about maces and mangling, if the undead is large, it will kill dwarfs, because you can hit an undead water buffalo in the head with a mace and it just bruises it.
In an animating biome, use cage trap choke points in your fort to handle random things, like old age pet deaths. So if you have an up/down staircase running through your fort, at every level, you should have a chokepoint with cage traps. A few hatchcovers is helpful too. The butchers area should be enclosed with cage trap chokepoints, and should be in a separate burrow so it can be removed during a civ alert, then if there are a dozen dwarfs fighting the llama wool that is tickling them, they will run away when the civ alert is triggered. Even the exhausted dwarfs will eventually get up and get out without being hurt by the wool.