Just as psychicscubadiver stated, not only do I think the Switch will beat the PSP, but the 3DS also has a chance for depending on how much longer Nintendo supports it. At the conclusion of the year, the 3DS should be somewhere between 74-75 million units sold and between 75-76 million units shipped.
The last shipment number I heard of for the PSP was 82 million. https://m.ign.com/articles/2014/11/17/vita-sales-are-picking-up-thanks-to-ps4-remote-play
82 million PSPs in the wild can be taken many as either shipped or sold. That is some odd phrasing, but dor now Ill say its shipped and the 80.8 million VGC has is sold.
That would mean the 3DS would have between 6-7 million million units left to ship and sell to catch it.
Difficult, even unlikely, but its not impossible.
Pancho A. Ovies
Nintendo Switch in Japan (Famitsu): 2018 vs. 2019
PlayStation 4/Xbox One/Nintendo Switch: 2018 vs. 2019