Oracles and Inquisitors can be extrapolated from how sorcerers and bards prepare their spells, as Oracles and Inquisitors aren't mentioned in the core rules for preparation time:
Each day, sorcerers and bards must focus their minds on the task of
casting their spells. A sorcerer or bard needs 8 hours of rest (just
like a wizard), after which she spends 15 minutes concentrating. (A
bard must sing, recite, or play an instrument of some kind while
concentrating.) During this period, the sorcerer or bard readies her
mind to cast her daily allotment of spells. Without such a period to
refresh herself, the character does not regain the spell slots she
used up the day before.
Oracles:
Unlike a cleric, an oracle need not prepare her spells in advance. She
can cast any spell she knows at any time, assuming she has not yet
used up her spells per day for that spell level. Oracles do not need
to provide a divine focus to cast spells that list divine focus (DF)
as part of the components.
Inquisitors:
An inquisitor casts divine spells drawn from the inquisitor spell
list. She can cast any spell she knows at any time without preparing
it ahead of time, assuming she has not yet used up her allotment of
spells per day for the spell’s level.
Oracles and Inquisitors are subclasses of Cleric, as Bards and Sorcerers are subclasses of Wizard (sort of!)
Cleric
Clerics meditate or pray for their spells. Each cleric must choose a
time when she must spend 1 hour each day in quiet contemplation or
supplication to regain her daily allotment of spells. A cleric may
prepare and cast any spell on the cleric spell list, provided that she
can cast spells of that level, but she must choose which spells to
prepare during her daily meditation.
Note also that Sorcerers also have the same sort of preparation quote text:
Unlike a wizard or a cleric, a sorcerer need not prepare her spells in
advance. She can cast any spell she knows at any time, assuming she
has not yet used up her spells per day for that spell level.
I would, therefore, suggest that these classes refresh in a similar way to their quasi-parent class:
Sorcerers need 8 hours of sleep and 15 mins concentration then they have their new spells.
Oracles and Inquisitors need to wait until the special "refresh time" and then spend 15 mins in prayer and then they have their new spells.
If you are not bypassing the spell prereq for the item, you are forced to 'cast' it.
http://paizo.com/prd/magicItems/magicItemCreation.html
From the creating wonderous item section (similar text can be found in almost all other feat specific sections).
If spells are involved in the prerequisites for making the item, the
creator must have prepared the spells to be cast (or must know the
spells, in the case of a sorcerer or bard) but need not provide any
material components or focuses the spells require. The act of working
on the item triggers the prepared spells, making them unavailable for
casting during each day of the item's creation. (That is, those spell
slots are expended from the caster's currently prepared spells, just
as if they had been cast.)
so in your case, each day you spent crafting the belt, you would need to use a copy of the scroll or have someone around who can cast it for you. Otherwise, you have to add +5 to the DC of the check.
Best Answer
For convenience, lets assign names to the two styles of item creation.
You don't combine the two. During an adventuring day 2 hours of progress is made on the stuff, or if capable of getting away for at least 4 hours, 4 hours of progress is made on the stuff. A high-level wizard who teleports from the dungeon to his lab or hauls his portable workshop into his mage's mansion and crafts away for 4 hours definitionally isn't out adventuring the whole day--he's spent part of it crafting! He won't get the free 2 hours per day, but he will get the whole 4 hours (barring interruptions).
The idea is to permit PCs who take item creation feats to use those feats even in a fast-moving campaign. If you're the wizard on Team Fighter, for example, the rest of Team Fighter can just keep on going day after day without stopping, and if you want to accompany them on all their adventures, you'll never have time to scribe a scroll. The casual item creation rule let you scribe a scroll despite not having time or facilities available for dedicated item creation, albeit at a vastly slowed rate.