Looking at it based on my experience, it is compliant to US TSA requirements with an asterisk "*" the caveat is that any decisions as to what is "OK" is up to the individual TSA agent. If they deem something to not be OK, then it does not travel. Sounds fishy, but if you tell me a knife blade under 2" is OK, I can find some pretty gruesome and dangerous 2" blades, so some discretion by TSA agents is needed.
There may be another issue though, you will also have to deal with European Security requirements, at least on the way back, but maybe if you have a security check en-route or take domestic flights within Europe. While the TSA generally allows corkscrews, for some reason the Europeans are more particular and generally do not. You can go online to see advice from any airlines you might be flying. The EU has a general guideline of "any sharp objects that might be used as a weapon" and they specifically mention corkscrews.
So in summary, you are likely mostly OK, but you never know what the agent you are running into is going to do, so a risk? Yes, but not a big one.
Myself, I happened to find a plastic corkscrew and bottle opener that stays in my carry on full time, with never an issue in a dozen trips. For silverware, I either pocket the ones one the trip over or stop in a grocery store and pick up a pack of mixed plastic utensils, plus maybe a small paring knife for more serious cutting. Sadly bringing a Swiss army knife is a thing of the past, unless I buy one there and give to the grandkids on return (putting in checked baggage on the way back)