Is it possible to weld multiple parts to my player's hand without finding the exact positions?

You can easily do this by iterating through all the parts under the weapon, and welding each of them.

local tool = script.Parent

-- make sure the parts are anchored before you run this function on them
function weldChildren(parent, p1)
    -- parent is the parent of the children that you want to weld
    -- p1 is the part each of the parts is going to be welded tonumber
    for _, v in pairs(parent:GetChildren()) do
        if v:IsA("BasePart") then -- make sure its a basepart so it doesn't error
            local weld = Instance.new("Weld")
            v.TopSurface = 0
            v.BottomSurface = 0 -- make sure they are smooth surfaces to avoid bugs
            weld.Parent = v
            weld.Part0 = v
            weld.Part1 = p1
            --CFrame of part1 relative to part0
            weld.C0 = v.CFrame:inverse() * p1.CFrame
            v.Anchored = false -- make sure that the parts are not anchored
        end
    end
end

weldChildren(tool, tool.Handle) -- calling function assuming tool is the tool, and tool.Handle is the part you want all parts to be welded to

And yes, you can animate it using animation editor

Hope it helped, if you have any further questions don't hesitate to ask.