Personally, I would recommend going larger on something like this so that you aren't near the maximum capacity and stressing the supply which could lead to early failure. I've found over the years with electronics that its better to have some reserve capacity vs operating near or at the max limits. That 10A power brick would only be able to deliver 120W and if the 160W PicoPSU ever needs more than 120W, like during the server starting up, then the power brick will be drawn over its limits.
As another alternative to a 10A power brick, here's a link to one that can deliver up to 20A (240W). With a power brick like this you shouldn't ever have to worry, even if the PicoPSU momentarily spikes to 160W or even higher, the brick will have a 50% reserve above the 160W max.
https://www.amazon.com/LEDwholesale...c5e60&pd_rd_wg=LV1ov&pd_rd_i=B074GGMD5J&psc=1
https://www.amazon.com/LEDwholesale...c5e60&pd_rd_wg=LV1ov&pd_rd_i=B074GGMD5J&psc=1
The only downside I see with this larger power brick are its physical dimensions look to be too large to fit inside the server. That may or may not be an issue depending on your goals around the server's appearance and extra wiring/cords.