God has provided us with a scripture that is complete, perfect and fully detailed. And we know through God's scripture that NOTHING shall abrogate His words.
[6:115] The word of your Lord is complete, in truth and justice. Nothing shall abrogate His words. He is the Hearer, the Omniscient. We also know that Quran is our only valid and divine source of law.
Which Hadith? [45:6] These are GOD's revelations that we recite to you truthfully. In which Hadith other than GOD and His revelations do they believe?
Everything needed for our salvation is contained in the Quran.
[6:51] And preach with this (Quran) to those who reverence the summoning before their Lord - they have none beside Him as a Lord and Master, nor an intercessor - that they may attain salvation.
Traditionalists have made up their own books called Hadith and Sunna which were NOT said by the prophet. In these fabricated books; there are many many prohibitions that were not prohibited by God. God tells us that He doesn't run out of words, therefore God doesn't forget to let us know what is prohibited and what isn't.
The Quran: Everything We Need [18:109] Say, "If the ocean were ink for the words of my Lord, the ocean would run out, before the words of my Lord run out, even if we double the ink supply."
If we are to prohibit anything beside what God has given us, we would be setting up other sources besides God's scripture and therefore fall into the category of idol worship.
Quran: Fully Detailed* [6:114] Shall I seek other than GOD as a source of law, when He has revealed to you this book fully detailed?* Those who received the scripture recognize that it has been revealed from your Lord, truthfully. You shall not harbor any doubt. *6:113-115 Upholding any source beside the Quran reflects disbelief in the Quran (Appendix 18).
Traditionalists prohibit many things including growing out your nails, wearing wigs, tattoos, piercing, etc. Many people would start asking why are they really prohibited. However I do not find anything in God's infallible scripture that prohibits such things.
However, God does tell us to maintain our modesty:
You Shall Dress Modestly [24:60] The elderly women who do not expect to get married commit nothing wrong by relaxing their dress code, provided they do not reveal too much of their bodies. To maintain modesty is better for them. GOD is Hearer, Knower.
God also tells us to subdue our eyes, having flamboyant tattoos and piercing may provide lots of eyes to be focused on the individual:
Dress Code for Believers [24:30] Tell the believing men that they shall subdue their eyes (and not stare at the women), and to maintain their chastity. This is purer for them. GOD is fully Cognizant of everything they do.
God also doesn't like show-offs or people that are just obnoxiously loud:
[8:47] Do not be like those who left their homes grudgingly, only to show off, and in fact discouraged others from following the path of GOD. GOD is fully aware of everything they do.
Most of all, God tells us to not to expose yourself too much. In my opinion this doesn't only refer to the dress code, but also to walk humbly (don't stick yourself out purposely from a crowd) and not to be obnoxious (which is another sense of having yourself sticking out of a crowd)
[31:18] "You shall not treat the people with arrogance, nor shall you roam the earth proudly. GOD does not like the arrogant showoffs.
[31:19] "Walk humbly and lower your voice - the ugliest voice is the donkey's voice."
Again, none of these verses actually tell us that piercing or tattoos are prohibited. However, these verses teach us some basic social guidelines. We need not to have ourselves sticking out of a crowd (in a sense to showoff or to expose yourself more) We need to be modest, and try our very best not to show off ourselves.
Overall, piercing/tattoos are not prohibited in the Quran. However, we need to decide for ourselves what would be socially acceptable/appropriate and what wouldn't in the light of the context of the whole Quran.