Would it be possible to manifest a weapon that has either the Silvered or the Adamantine property?
Per the description of Pact of the Blade:
You can use your action to create a pact weapon in your empty hand. You can choose the form that this melee weapon takes each time you create it (see chapter 5 for weapon options).
Chapter 5 in the Players Handbook is about Equipment; including Weapons. Within weapons there is a subsection on Silvered Weapons.
Some monsters that have immunity or resistance to nonmagical weapons are susceptible to silver weapons, so cautious adventurers invest extra coin to plate their weapons with silver. You can silver a single weapon or ten pieces of ammunition for 100 gp. This cost represents not only the price of the silver, but the time and expertise needed to add silver to the weapon without making it less effective.
If this was a physical thing, then it would require spending money for the silvering process. But this is a weapon created from the mind of the wielder and formed from Shadow.
Note: I understand that silvering a weapon is used to overcome resistance and the manifested weapon is considered magical which generally overcomes the same resistance. But I could envision a monster that is actually vulnerable to silver so silvering it would be a boon beyond just being magical.
Also, if a weapon has the Adamantine property it becomes better at breaking objects. Another bonus above just being magical.
Best Answer
No, as silvered and adamantine weapons are not items that are directly mentioned in chapter 5
You have already quoted the relevant section, which states that you have to see chapter 5 for your weapon options. Within chapter 5 it describes the ability to silver weapons, but does not specify any particular silvered weapons. It does not even mention adamantine weaponry. As such, only the mundane weapons are permitted.