I don’t remember the last time that I played with a doorbell, so I cannot speak to the specifics. I can, however, give you some design and application generalities and what I would do.
Short answer: Safety issues would be fire from overloading and overheating of the transformer. I’d just replace the trans with the correct one; it’s a doorbell transformer, they are not expensive.
Long answer: when manufacturers rate their equipment, it is never at the absolute maximum that the equipment can withstand. There is some cushion in there, as far as the transformer goes. The same can be said for the chimes, just in reverse: their power ratings are what they would like to see, but in the real world they will use less power than what the rating calls for.
However, the equipment does have a rating for a reason. And although you are dealing with voltages that are considered safe and thereby not going to shock you to where it would injure you, the larger problem is actually overloading and overheating of the transformer.
I was going to get into the math of it all, but that would just be overkill, I think. Essentially, your new chimes call for twice as much power as the transformer is capable of putting out. Will it be a problem? Probably not - how often does a doorbell actually get used?
But, for the $20 or $30 and the 15 minutes to change it, it isn’t worth the risk of potential fire. My two cents, take it for what it is worth.
Your providing half the power the unit wants (or your transformer is rated to deliver 1/2 the watts (VA) needed)
Worst case - the transformer is capable of providing my amps than rated, and you push it and it overheats and catches fire – I would put that at very low risk.
more likely your chime is working outside its power spec, and that can cause long term issues, so your shortening the life of the chime.