Firstly, I want to address the Infinity Gauntlet part of the question as that is answered here. The user needs to make a fist with the Infinity Gauntlet to be able to use it. Whilst this restriction was placed out of universe it is not inconceivable that Eitri baked the restriction in as a minor hindrance to Thanos and to give others a chance against him.
“As you can imagine, when you have a gauntlet that has nearly unlimited power, and every time you use it you can do what you want ... we wanted to create small physical rules that would allow people to hang in a fight with him, so the idea that he had to, you know, close his fist to use a stone was the bare minimum that allowed us to have a fight,” McFeely said.
comicbook, ‘Avengers: Infinity War’ Writer Explains the One Catch Behind Thanos Using the Stones
Aside from that there doesn't appear to be any restrictions, every other object appears to pass the Infinity Stone's power right through it. For example, it doesn't seem to matter where Ronan holds his Cosmic rod or where Loki is holding his Scepter or where anyone holds the Tesseract. As long as they are holding the object that the Infinity Stone is in they can harness its power.
The only odd one out here would be the Orb for the Power Stone. However, the Orb seems to have been built with the specific task of housing the Power Stone to stop people from touching it and destroying the surroundings. I mean, we saw what happened to Carina in Guardians of the Galaxy. The Power Stone is very capable of destruction before you even think about actually trying to control it so it makes sense it is hidden away in a device that is there to hide the power within from being used and harnessed.