Not only will the Switch pass it (unless sales somehow fall off a cliff), but I think the 3DS has a shot to pass the mark also. It currently sits at 73 million and only needs another 8 million to do it. I realize that the 3DS is near the end of its life and Nintendo is putting resources towards the Switch, but so long as they continue to produce units and give it at least second tier support it could last just long enough. Sony abandoned the PS Vita years ago and it still managed to sell almost 20% of its final total in those twilight years (~3 million sold 2016-2018 out of 16 million total).
I don't know if the 3DS can make it to 81 million... However there's no way the Switch will sell less than the 3DS.
That's why I think Switch will outsell the PSP. At this rate it's just a matter of time (Unless sales fall off a cliff, like you said).