Reducing Alar Base Without Reducing Nostril Size?

It is possible to perform an alar base reduction without changing the nostril size.
There are several techniques for addressing the nostril (alar) base. It is possible to change the amount of flare, distance from one nostril rim to the other, width of the columella, nostril size, nostril shape, hanging ala and nostril thickness.
Each one of these variables can be addressed separately or in combination to produce a nostril base that is in balance and harmony with the rest of the nose.

Yes there is. Just make sure you get evaluated by a board certified plastic surgeon, who can go over the procedure with you and the incisions involved.
Make sure you are clear as to what you want to achieve and the surgeon can evaluate you and explain if what you are looking for is reasonable and surgically possible.
Good luck.

When dealing with a circular structure, any reduction in the perimeter will affect the the overall size of the circle.

Therefore, your answer is no, surgical reduction of nasal base will reduce and change the nostril size, however, cinching of the nostrils with suture alone will temporarily  bring the nasal lobules together but will cause the nose look over projected.