Is it possible to accomplish this without having to use RayCasting?

Thanks to Crazyman32 for creating a Module Script

Here the ModelScript You will need to create in the same folder as your localScript

ModuleScript

local Mouse = {}
Mouse.__index = Mouse
function Mouse.new()
	local player = game.Players.LocalPlayer
	assert(player, "Could not get player")
	local cam = game.Workspace.CurrentCamera
	local Ray = Ray.new
	local input = game:GetService("UserInputService")
		local button1 = Enum.UserInputType.MouseButton1
		local button2 = Enum.UserInputType.MouseButton2
		local button3 = Enum.UserInputType.MouseButton3
		local mouseMovement = Enum.UserInputType.MouseMovement
		local mouseWheel = Enum.UserInputType.MouseWheel
	local mouse = {}
	local mousePos, mouseDelta = Vector2.new(), Vector2.new()
	local clicking = {
		[button1] = false;
		[button2] = false;
		[button3] = false;
	}
	local function CreateEvent(eventName)
		local e = Instance.new("BindableEvent")
		mouse[eventName] = e.Event
		return function(...)
			e:Fire(...)
		end
	end
	-- Events ---------------------------------------------------------------
	local buttonDown = CreateEvent("ButtonDown")
	local buttonUp = CreateEvent("ButtonUp")
	local moved = CreateEvent("Moved")
	local scrolled = CreateEvent("Scrolled")
	-------------------------------------------------------------------------
	-- API ------------------------------------------------------------------
	function mouse:IsDown(inputType)
		return (clicking[inputType] == true)
	end
	function mouse:GetPosition()
		return mousePos, mouseDelta
	end
	function mouse:ProjectMouseRay(ignoreList)
		local pos = self:GetPosition()
		local ray = cam:ScreenPointToRay(pos.X, pos.Y, 0)
		ray = Ray(ray.Origin, (ray.Unit.Direction * 999))
		local hit, hitPos, normal = game.Workspace:FindPartOnRayWithIgnoreList(ray, ignoreList or {}, true, false)
		local cframe = CFrame.new(hitPos, (hitPos + ray.Unit.Direction))
		return cframe, hit, normal
	end
	-------------------------------------------------------------------------
	-- UserInputService Setup -----------------------------------------------
	local function InputBegan(inputObject, gameProcessed)
		if (gameProcessed) then return end
		local inputType = inputObject.UserInputType
		if (inputType == button1 or inputType == button2 or inputType == button3) then
			clicking[inputType] = true
			buttonDown(inputType)
		end
	end
	local function InputChanged(inputObject, gameProcessed)
		--if (gameProcessed) then return end
		local inputType = inputObject.UserInputType
		if (inputType == mouseMovement) then
			local newMousePos = Vector2.new(inputObject.Position.X, inputObject.Position.Y)
			local delta = newMousePos - mousePos
			mousePos = newMousePos
			mouseDelta = Vector2.new(delta.X, delta.Y)
			moved(mousePos, mouseDelta)
		elseif (inputType == mouseWheel) then
			local num = inputObject.Position.Z
			scrolled(num < 0 and -1 or num > 0 and 1 or 0)
		end
	end
	local function InputEnded(inputObject, gameProcessed)
		--if (gameProcessed) then return end
		local inputType = inputObject.UserInputType
		if (inputType == button1 or inputType == button2 or inputType == button3) then
			clicking[inputType] = false
			buttonUp(inputType)
		end
	end
	input.InputBegan:connect(InputBegan)
	input.InputChanged:connect(InputChanged)
	input.InputEnded:connect(InputEnded)
	-------------------------------------------------------------------------
	return setmetatable(mouse, Mouse)
end
function Mouse:__tostring()
	local pos = self:GetPosition()
	return ("Mouse <" .. tostring(pos) .. ">")
end
return Mouse

and here is a edited version of your localScript

local mouse = require(script.Parent:WaitForChild("ModuleScript")).new() -- here we request it 

local modelMode = false

local player = game.Players.LocalPlayer


local selection = Instance.new("SelectionBox")
selection.Color3 = Color3.new(0,0,5)
selection.Parent = player.PlayerGui


mouse.Moved:connect(function()
local cframeHit, target, surfaceNormal = mouse:ProjectMouseRay() -- here we use the modeleScript to get the target


    if not target then
        selection.Adornee = nil
    elseif modelMode then
        if target.Parent:IsA("Model") then
            selection.Adornee = target.Parent
        elseif target.Parent.Parent:IsA("Accoutrement") then
            selection.Adornee = target.Parent.Parent
        elseif target:IsA("BasePart") then
            selection.Adornee = target
        else
            selection.Adornee = nil
        end
    else
        if target:IsA("BasePart") then
            selection.Adornee = target
        else
            selection.Adornee = nil
        end
    end
end)

I hope this will solve your problem :D And no there is no other way to solve this without using ray casting