You have the choice to really do what you want when it comes to manufacturing, after all you are the customer and can do what you please. If you choose to or feel you can do a better job with assembly and packaging then you have the choice to just ship over the individual parts and assemble them yourself.
Assembly yourself will be a time consuming exercise and but if you have time then the perfect opportunity to save some money. Remember you cannot do the job more efficiently than a team of people working on an assembly line and for the extra assembly procedure could cost cents in the long run.
My suggestion is to let the manufacturer do the assembly, like i said it will cost a fraction of the price of your product and will free up time for you to do more important things like marketing.
If peace of mind is what you want then you always have the opportunity to fly to your manufacture and arrange quality procedures with them to suit your needs.
You will always feel you can do a better job but once you finalise your quality control then there is no excuses for the manufacture to product poor parts. If they do then you have the right to refuse their parts and request more to the quality you require.