How can I use a portable A/C unit to cool my clean room?
I've seen several unique installations of portable type air conditioners. The true difficulty comes as you need to have a separate location to exhaust, which will get both hotter and more humid. Fundamentally, an air conditioner is increasing the temperature gradient between the cooled side and the exhaust side. This exhaust side is typically meant to be outside, as the way most of these uprights are built, blows a healthy majority of condensate out as water vapor. I discovered this after I disassembled mine completely out of curiosity.

To get more directly to your question, unless you have a good and thorough seal between the area you're cooling and area your exhausting to, you will actually just be disturbing more air and creating some odd microclimates.

It matters less if you pipe the exhaust out, or if you pipe the cooled air in. What matters is that you contain the cooled air and prevent it from re-mixing with the unconditioned air.

However, these units can create a bit of negative pressure near them as they  exhaust some air from the conditioned space, over the heat exchanger. So your suspicion that it is pulling in the air from your shop that it sounds like is both unconditioned AND it sounds like you're exhausting to.

I would surmise, that creating a positive pressure from blowing in the conditioned air might feel more comfortable, but know that you're creating a fairly small space with both a dry cool area and a warmer, more humid area. This could cause problems with things like condensation, mildew, corrosion, etc. if there were enough moisture throughout.

It might be good to pair this with a dedicated dehumidifier also.

Also, it's worth noting, that the recovery time for these type of units is quite poor. It makes more sense to let them run as much as possible, and the larger/more hot and muggy the room you're conditioning, the more lead time they'll require.

I would also go ahead and check how the exhaust vent line is attached. If it's misaligned, has a tear etc, you would just be blowing heated and moistened air near your unit.