The specificity of the Pathfinder rules imply it's impossible to move your normal speed while stealthing, in addition to while attacking, running, or charging.

Note that Paizo is currently playtesting new Stealth rules that cover this situation:

You can move up to half your normal speed and use Stealth at no penalty. When moving at a speed greater than half and up to your normal speed, you take a –5 penalty.

Creating a diversion to hide

While it's mentioned as part of both the skills Bluff and Stealth, creating a diversion is detailed under the Influence skill (a combination of Bluff, Diplomacy, and Intimidate) in Pathfinder Unchained (released about 5 years after the Pathfinder Core Rulebook). To create a diversion to hide, you take a standard action, "attempt[ing] an Influence [i.e. Bluff] check against the viewer’s opposed [S]ense [M]otive [check]. If you succeed, you can attempt a Stealth check. When applicable, use the same modifiers from the lie function."

The inquisitor archetype heretic when using the supernatural ability judgment can opt for the escape judgment to grant the inquisitor the ability to take a move action (instead of a standard action) to create a diversion to hide upon making a successful attack. This lets the inquisitor, essentially, stab then hide.

(From an optimization perspective, this is acceptable at low levels, but it'll lose its luster at higher levels when full attacks are necessary to pull your weight. Further, picking the escape judgment typically means forgoing all the other awesome judgments the inquisitor could've picked instead! And the issue remains that the inquisitor still needs to end her movement behind cover or in concealment to have stealth and those conditions must be within 15 ft. of her unless she can afford suffering some hefty penalties. Also, if she has the supernatural ability hide in plain sight, that ability is just super better than this one.)

Becoming invisible as a spell-like ability

The complete text of the inquisitor's clandestine inquisition's granted power disappear, a spell-like ability, says, "You can become invisible as per the spell as a standard action. The invisibility lasts for 1 round per inquisitor level or until you attack. You can use this ability a number of times per day equal to 3 + your Wisdom modifier." Typically, a creature can only take 1 standard action per round. Thus a normal creature that takes the standard action to activate the spell-like ability disappear will be unable to also attack in the same turn. (She'll also provoke an attack of opportunity from each foe threatening her when she activates the spell-like ability disappear, by the way. Follow this link and this link to learn more about the differences between spells, spell-like abilities, and supernatural abilities.)

Sniping and hiding in plain sight

The special case with sniping is that after making that one ranged attack the sniper can take a move action to remain in the same place and, if the sniper's Stealth skill check to hide result (that suffers a −20 penalty) beats onlookers' Perception skill check results, the sniper need not move, the sniper's position undetected by onlookers. Snipers do this—stay in one place—because normally "Stealth immediately ends after [the sniper] make[s] an attack roll, whether or not the attack is successful." While the sniper—instead of sniping—could have just make an attack from her originally-hidden-but-revealed-upon-making-the-attack position then take a move action to move from that position, that'd mean everybody sees where she is and where she's going!

However, with the shadowdancer's supernatural ability hide in plain sight and without using the sniping rules, the sniper's position is still revealed after the attack, but, afterward, the sniper can take a normal move action (or even a 5-ft. step) in conjunction with the skill Stealth to take up a different position. (She can't stay in the same place because everybody knows she's right there because she revealed her position by making an attack!) She makes a Stealth skill check opposed by observers' Perception skill check "even while being observed." Further, "[a]s long as she is within 10 feet of an area of dim light, a shadowdancer can hide herself from view in the open without anything to actually hide behind."

This means a shadowdancer sniper in, for example, a cramped pillbox likely must use the normal sniping rules, but, if out in the open, the shadowdancer will be better off using the supernatural ability hide in plain sight.

Note: You've picked to play a minigame that, traditionally, Pathfinder doesn't play well. If you want to play a good, interesting stealth simulator, you may find Pathfinder disappointing you, and you may find the GM frustrated by your efforts to fit this square stealth peg into that round just-fight-stuff-normally-already! hole. There's a lot of confusion around the issue of stealth, and it's been the subject of long debates, frequent animosity, and at least a few official revisions. If everyone at the table objects to this particular playstyle, keep in mind for your next character that the game is a much more robust magic simulator and smacking-things-with-swords simulator.