Very easy to do:
This video https://www.youtube.com/watch?v=NpMYZq-qQNo shows an EASY way to get the voice coil centered. You don't need to use any shims and you will not need to remove the dust cap. This method uses a PC or a phone and a free app to produce a 50 Hz signal that you can use to be sure the voice coil is not scraping or rubbing as you are gluing the surround down to the speaker frame. I have done this several times and it works great. Most of the time the paper cone seems to almost center itself. You have to choose the correct type of glue. For many cones ( paper) Aleene's Original Tacky Glue works well. this is easy to find an inexpensive. But you say that you have a plastic cone, and if this is polypropylene then that is much more difficult to glue to. See this reference: http://techtalk.parts-express.com/forum/tech-talk-forum/43449-glue-to-polypropoline The Aleene's tacky glue worked on this for me when I tried it on a plastic cone, but it took a VERY LONG time to get the surround to stay tacked down and I had to constantly be pressing down on parts of it that would lift up. If you search you may find a glue that works better on plastic, or go to one of the suppliers of surrounds and speaker repair kits and ask what glue they sell or recommend for plastic cones.
This video https://www.youtube.com/watch?v=NpMYZq-qQNo shows an EASY way to get the voice coil centered. You don't need to use any shims and you will not need to remove the dust cap. This method uses a PC or a phone and a free app to produce a 50 Hz signal that you can use to be sure the voice coil is not scraping or rubbing as you are gluing the surround down to the speaker frame. I have done this several times and it works great. Most of the time the paper cone seems to almost center itself. You have to choose the correct type of glue. For many cones ( paper) Aleene's Original Tacky Glue works well. this is easy to find an inexpensive. But you say that you have a plastic cone, and if this is polypropylene then that is much more difficult to glue to. See this reference: http://techtalk.parts-express.com/forum/tech-talk-forum/43449-glue-to-polypropoline The Aleene's tacky glue worked on this for me when I tried it on a plastic cone, but it took a VERY LONG time to get the surround to stay tacked down and I had to constantly be pressing down on parts of it that would lift up. If you search you may find a glue that works better on plastic, or go to one of the suppliers of surrounds and speaker repair kits and ask what glue they sell or recommend for plastic cones.