First off, welcome to the OB!
Now, since you can't post pics onto the OB until after 5 posts, and there are no pics of the orchid in question, it's difficult to say for certain whether the orchid needs to be repotted into a larger pot or not.
However...
I can say that there are most certainly clear plastic pots for sale that are the same dimensions as the pot that your orchid is currently in.
While it isn't 100% necessary to switch from an opaque plastic pot to a clear plastic pot, I will mention that it is a recommendation. I recommend the clear plastic pot for several reasons.
1. As a grower, you can partially see what is going on with the roots and how wet/dry the potting media is before watering again.
2. Allowing some of the roots to photosynthesize. You see, most epiphytical orchids (orchids that grow on trees), as well as some lithophytic orchids (orchids that grow on rocks), have roots that are capable of photosynthesis. This is the reason why when the roots of these epiphytical and lithophytic orchids are exposed to light, they are green.
On another note, I would also recommend removing your newly acquired orchid from its pot completely to examine the condition of the roots to see whether there are any dead or living roots. I believe that this is good practice for a beginner to get accustomed to check for certain what the condition of their orchid's roots really are instead of just taking a wild guess at it.
Changing the orchid into fresh media also is a plus, considering you don't know when the last time the orchid was repotted prior to reaching your home.
The new potting mix you described seems good enough for the orchid. However, because there are no photos of the old or new potting mixes either, it is difficult to tell you the quality of the mixes (i.e. how fresh the old/new mixes are, compared to how degraded the mixes look). As long as each piece of bark is medium to large grade in size, the Cattleya should be fine.
Since you mention the pot size being 2"x2"x2", I'm assuming that it is a seedling. Again, without knowing what the Cattleya is by name, it's difficult to tell whether it is a naturally miniature sized Cattleya or a seedling for certain.
Cattleyas are generally intermediate to warm growing (55 F - 95 F).
They appreciate moderate to high humidity (60% - 90%). High humidity is not absolutely necessary to grow a Cattleya well, but it doesn't hurt it either. A humidity range of roughly 60% - 70% is adequate enough.
Cattleyas are generally high light orchids. Grow them in indirect bright light. Unfortunately, I don't own a light meter, so I cannot give you a numerical value to assign a range of lighting that Cattleyas grow well in. I personally eyeball it.
If you have further questions, go ahead and ask.