The answer to any question like this is "it depends." Magic can do all sorts of things! However, most likely the demands exceed what most people would think a wizard could do.
The key challenge for the Wizard is to achieve criticality. This is a mixture of many factors such as mass, density, nearby neutron reflectors, and several others. When you achieve criticality it means the neutrons released from the fission of uranium atoms are sufficiently likely to collide with another uranium atom as to cause the entire mass to undergo fision.
This would be terribly hard to do with un-enriched uranium. The U-235 that undergoes fission is relatively low in concentration in naturally occuring uranium. This means you would have to crush the uranium far harder than we had to in an atomic bomb. If the wizards can create a pocket black-hole, they can probably make un-enriched uranium undergo fission. However, if they can make pocket black-holes, one must question if nuclear weapons are even interesting to the wizards!
Assuming they do have enriched uranium, in a suitable configuration, the next step is to crush it together. This is actually quite the dance in real nuclear weapons. Once the reaction starts, it naturally wants to expand. If you don't crush it in just the right shape, it will find a way out and much of the material will never get the chance to undergo fission. The initiators on a nuclear bomb are unique in their precision. They are several order of magnitude more exacting with their timing than any other initiator in the world. They have to be this precise to make sure the many shaped charges layered on top of each other create the proper lensing effects.
Our wizard would need to be able to create a similar level of uniform compression. This compression would need to be held against the nuclear bomb's own explosive forces. This is where believably is tricky. The wizard would certainly not have the timing needed to collapse it perfectly the way we do, so the wizard would have to rely on brute force, holding it together for even longer, while the bomb is exploding. A wizard that can do this can make your head pop off like squeezing a grape.
In the end, it will all come down to Sanderson's First Law:
Sanderson’s First Law of Magics: An author’s ability to solve conflict with magic is DIRECTLY PROPORTIONAL to how well the reader understands said magic.
If you have built up your story such that the reader understands how the wizard could attain such extravagant powers, then by all means have your wizards set off nuclear bombs!
Just brainstorming along the lines of the TV show Lost, perhaps your wizards have nearly limitless power, but are forbidden from directly using these powers to hurt people. Perhaps one evil wizard has found this nuclear bomb trick to be a technicality that skirts the rules.