Silicone lubes generaly dont react a lot on TPE. Most TPE doesnt even react at all (its a plastic, which if silicone would harm it, would probably also be harmfull towards its user. most silicone reactions are purely because its a similar material).
And strokes are usualy made with TPE as its sturdier and significantly cheaper. Only for things like vibrators silicone is still used as it gives just that little bit of a better feeling. Which only in vibrators matter since there the softness matters more. And even here, TPE is a popular replacement. TPE is very cheap (toy costs can easily be half of the price).
With it, manufacturers are even aware of typical usage of their vibrators, and prefered lubes. For anything ment for anal use, they are aware of potential silicone lube usage, so they design it with TPE or latex. And for women, since they already self lube, water based lubes are fine as they only are needed in the beginning.
This warning is mostly just ment to ensure people dont forget the potential risk and actualy check when they use it (in the EU it isnt even mandatory to warn anymore as the silicone toys themselve already provide the warning. but out of USA habits they still do anyway).
For me the handy sleeves over time become more stiff anyway (and also yellow over time). From my experience this is normal through use. The most used sleeves show this significantly more even. And transparent sleeves are already more vulnerable here (probably because UV light is a factor, which non transparent sleeves block). I would say that after about 6 months of regular usage a sleeve becomes worn too much anyway and is better to be replaced.
And as the handy sleeves arent too expensive, why not just test it anyway? If the lube damages the sleeves too fast, then you will know and potentialy just need to replace it faster, and if not you also know the lube is fine.
There is barely any risk when combining the lubes, since in the end, condom usage with TPE toys is already recommended for cleaning purposes (there is no advise against mixed usage, and technicaly also no risk when a condom breaks which definitely would cause mixed contact in lube/material/skin). There is no warning about silicone based lubes on the condoms there (the only reason for its condom recommendation is because TPE is poreous).
