You may be right. The Constitution is often very general and Congress may have established a practice which does require the President’s signature. I know there have been cases where a President pushed for a state to be admitted—West Virginia (illegally carved out of Virginia) and Nevada (to give the Republicans 3 more electoral votes in 1864—for decades Nevada’s total population was well below the 60,000 which had historically been required before a territory was granted statehood, although it may have briefly been over 60,000 in the 1860s because of the silver rush).
In the case of Nevada, I think the amount of silver being mined may well have counted more for statehood than the 3 EVs.