Yeah. For the spiders, this is gunna suck, but it’s not undoable. I do suspect it will be more of an exo-exoskeleton than a suit though.
There’s a couple of reasons why it won’t be particularly pleasant. The first has to do with how unbelievably sensitive spiders are. Their bodies are covered in a variety of specialised hair like structures that give them not one but two extra senses, and they’ve got extra bits in their knees that give them yet another one. The suit is basically going to annihilate any option of using those (especially the hairs for sensing air motion, which in some spiders are sensitive enough to pick up on the pressure caused by a laser pointer). It’d be like someone shining a light into your eyeball, but body wide.
Depending on whether or not these extra senses have survived into your modern spiders and how strong they are you may need training, drugs or both in order to deal with the suits (as some people may need anti-nausea drugs to deal with zero-G)
The second reason it would either suck or need some exceptional engineering is that terrestrial spiders breathe via almost all of their body. They don’t have particularly dedicated airways or efficient circulatory systems and as such are used to being surrounded by air in order to get enough oxygen into their vital organs. In other words: you need to keep a flow of air between the suit and the spider or they will suffer from the equivalent of hypoxia (which can be thoroughly unpleasant).
That might not seem like an issue, but it really is. Anything pressurised in space will want to puff up like a balloon. That stops you from moving limbs, severely restricting motion. The only way to deal with it is to have rigid ‘space armour’ that air can flow under without deforming the suit, and that comes with a whole extra set of challenges around mobility/cooling. Not only that but you’ll have to have pump air around the suit in order to keep it oxygenated. Pumps vibrate.
Remember those weird knees I mentioned earlier? They’re super-sensitive vibration sensors. To the poor spider inside this vibrating, solid tin can it’s gunna be thoroughly unpleasant.
Manipulators are simple at least as spiders don’t have dexterous fingers to worry about. As such ‘bond villian’ claws can be added to the ends of the suit and operated using simple squeeze actuators without being too weird. Or you could replace with a variety of simple tools. And any suit umbilicals also have a natural attachment point near the spinnerettes where they can be grasped by hind legs.
So basically: armoured, mechanically clawed, permanently on edge spiders floating through space.