I had the same problem, but for me only one mounting hole didnt work so i didnt want to take the risk.I have an rx 570 nitro which sounds like a small card but i assure its huge,the cooler is larger than some laptops and heavier.
So i bought 2.5mm screws and a 5 size wrench(i live in Romania,idk what key size it would be for that size screw).there are wrenches for these small sizes.It doesnt work as well with the finger,except if you use rubber gloves that have better grip.Medical latex gloves work probably.But dont screw them in incredibly tight,like crazy tight,but secure them safely in place,tighten them very well,but dont overdo it i think(im not sure you can,but just to be safe).You cant overtighten them with latex gloves,but if you do it with a small wrench you might,idk.
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Here are the pics.
They are very tight,i also added a elastic grover washer which takes care of the vibration better.
Its much better than with the original screws.I basically put in normal screws and nuts and washers and it works great.
I think it would work with a 3mm screw,but i thought its kind of too tight of a fit so i went with a 2,5 mm one and they work great.You dont need such a long screw,like the ones i have there,but the diameter only.Thats the only length screws i could find at that diameter.
Here is a transformation table between us sizes and mm
https://www.boltdepot.com/fastener-information/Metric-US-Conversion-Table.aspx
Idk how accurate this is.But its prob good.
And to your question as to whether its safe to leave it without being screwed in,i would say that most definetely no,it isnt.Especially now when if it breaks a 1650 is like 400 dollars,because of lack of stocks(scalpers+miners have caused massive inflation of prices so take care of your card).It could also break your motherboard,so no it isnt safe.
Do what i did,put normal screws and nuts and washers and it works great,better than before.