Yes, but only if you sterilise it properly, by taking it to a piercing shop which will autoclave it for you. The link posted by @Jeruba seems to be based on how to sterilise a needle which hasn’t been used by anyone else. Googling alcohol + blood borne pathogens should give you lots of information indicating that the method outlined there is inadequate.
To be honest, although I understand your desire to minimise your consumption of new jewellery and tapers for environmental reasons it might be best to just buy new for safety reasons and also because I’ve always found it very useful to have smaller sizes of jewellery in reserve. You never know when you might need to downsize for any number of reasons, and having the appropriate jewellery on hand is really useful.