Is wearing uranium glass safe?
No. It's not safe. You need to send it to me. I am a trained professional.
Just kidding. It's perfectly safe. A piece of uranium glass jewelry will barely exceed background radiation levels if it does at all. You get exposed to more radiation from flying in a plane, hiking in a canyon with a lot of granite, fertilizing your garden, or even eating a banana. Also, uranium is primarily an alpha radiation emitter, which cannot pass through skin.
Here are some sources with good info on the safety of uranium glass -
"Glass: glassware, especially antique glassware with a yellow or greenish color, can contain easily detectable quantities of uranium. Such uranium-containing glass is often referred to as canary or vaseline glass. In part, collectors like uranium glass for the attractive glow that is produced when the glass is exposed to a black light. Even ordinary glass can contain high-enough levels of potassium-40 or thorium-232 to be detectable with a survey instrument. However, the radiation received when using glassware – even canary or vaseline glass – is unlikely to exceed background radiation levels." (Source: Environmental Protection Agency, https://www.epa.gov/radiation/what-kinds-consumer-products-contain-radioactive-materials)
To exceed the yearly dose of allowable radiation, which measured in hours is 114 nSv/hour, you would have to wear multiple large uranium glass necklaces and bracelets 24 hours a day every day of the year (the study uses a glass plate, so this is based on an equivalent amount of glass, and this is with the assumption that the glass jewelry pieces have measurable radiation, when most do not) . (Source: Study by Prof. Dr. Gerhard Billek, Hamburg - https://www.uranglas.ch/wp-content/uploads/2018/11/Strahlenbelastung_Uranglas-1.pdf)
Study of uranium glass objects determined to be within background radiation values
https://www.sciencedirect.com/science/article/abs/pii/S129620740800099X?via%3Dihub
Drinking out of this glass (their math was done at 10% presence of uranium) and storing items in them, gives a max exposure per person of "this individual could receive an annual EDE of about 1.8×10-3 mrem [that's 0.0018 mrem] from ingestion of uranium leached from glassware." That's exclusively drinking out of these glasses (290 L/yr) and storing drinks in containers as well. And that is less than two-thousandths of a single mrem. The addition of handling and washing the glasses: "Thus a highly exposed individual could receive a total EDE of approximately 2 mrem/yr of glassware use."For having items on display in a home, again at 10% uranium presence, with specifics of 4 pieces on display throughout the home- how many hours/yr they are handled - etc, "This individual could receive an EDE of 0.2 mrem/yr." That means if you had 400 glassware pieces (as a collector might end up with) you might be getting 20 mrem/yr in exposure. For comparison, you can get 12 mrem from a round-trip flight from LA to NY. You get 2 mrem/yr from watching 4 hours of TV per day. You get 10 mrem/yr from eating lots of bananas. You get an additional 50 mrem/yr exposure from living at a higher elevation (Denver vs sea level). Max recommended is no more than 5,000 mrem in any one a year - and no more than 1,000 mrem per year of life (so not over 40,000 mrem by age 40, etc) in addition to the ~300 mrem you already get in a year. (Source: United States Nuclear Regulatory Commission: Systematic Radiological Assessment of Exemptions for Source and Byproduct Materials - https://www.nrc.gov/reading-rm/doc-collections/nuregs/staff/sr1717/)
As you can see, the amount of radiation exposure that can come from UG jewelry is a fraction of a fraction of levels that can affect your body.

Uranium glass sculpture at the Museum of Jewelry and Glass in Jablonec, Czech Republic