Here’s a sample Bastard Sword, with weight given as 3.1lbs (1.4kg). A Uranium sword would therefore weigh approximately 7.4lbs (3.4kg). Probably very awkward for a real swordsman, but nothing you couldn’t get accustomed to with training. It wouldn’t make for very deft parrying, though. Mighty barbarian warriors or evil Witch Kings (loved that morning star in ROTK, BTW), of course, wouldn’t be unduly inconvenienced.
This source asserts that U238 is normally slightly softer than steel, which is at odds with this site, which asserts that it is the second hardest common metal known, after Tungsten. Even given that the depleted uranium used in projectiles is subjected to a classified hardening process, it seems to be an open question just how hard the enriched uranium sword would be.
Of course, a sword slightly softer than steel would still be a pretty effective weapon. The Romans and Greeks did fine with iron and bronze, after all. Moreover, the increased mass of the uranium sword would make it cleave that much more effectively. If, as a natural characteristic or due to alloying or hardening, the uranium sword is also harder than steel, it’d likely perforate armor wonderfully.
The pyrophoric quality of depleted uranium only kicks in at about 500C. It enhances the effect of high velocity projectiles, which easily reach that temperature on impact, but would not make much difference to a sword. Granulated uranium’s pyrophoric qualities are accentuated, presumably because of increased oxygen exposure, and even friction. A sword would likely develop a “patina” that would limit further reactivity. However…
Another quality that makes depleted uranium desirable in projectiles is “adiabatic shear banding”. I.e., it’s self-sharpening. A uranium sword might therefore hold a wicked edge. Moreover, the pyrophoric qualities of particles lost on impact with an enemy’s sword or armor would make for a nicely showy spray of sparks, beyond what a sword fight would normally produce.
I’ve heard that even depleted uranium is slightly warm to the touch, so I expect that an enriched uranium sword would be as well, even if no fission activity was going on. All in all, I’d say go for it! Just be sure to wear a lead codpiece.