The Bladesinging Wizard gets the Training in War and Song feature, which states (SCAG, p. 142; emphasis mine):
[…] You gain proficiency with one type of one-handed melee weapon of your choice […]
Similarly, there is the Dual Wielder feat, which states (PHB, p. 165; emphasis mine):
[…] You can draw or stow two one-handed weapons when you would normally be able to draw or stow only one […]
Could a Wizard then choose the lance or Versatile weapon to gain proficiency in? (They can't choose the net because it's ranged.)
Could somebody with Dual Wielder draw/stow a lance, net, or Versatile weapon? None of them have the Two-Handed property, but they do have either the Special or Versatile properties so I'm unsure how this works out. Do nets and lances and Versatile weapons count as one-handed weapons?
The following question already exists but it only establishes that a lance while mounted counts as a one-handed weapon:
Best Answer
The rules implicitly assume that non-two-handed weapons are one-handed
The two-handed property says:
For weapons without the two-handed property, I can't find anything in the rules that directly says they are considered one-handed. However, although there is no explicit "one-handed" weapon property, there is strong circumstantial evidence that the designers consider all non-two-handed weapons to be one-handed weapons. First, the Crossbow Expert feat and the ammunition property both which make explicit reference to "one-handed weapons". In addition, the rules for melee attacks say:
Similarly, the rules for improvised weapons also reference holding the weapon in your hands:
And assuming that all PCs have 2 hands (which is currently the case for all official playable races), the only ways to wield a handheld weapon are with either 1 hand or 2.
Finally, a few official rulings in the Sage Advice Compendium also reference one-handed weapons, such as:
This ruling strongly implies that any non-two-handed weapon is considered a one-handed weapon, or else it wouldn't be eligible for two-weapon fighting. In general, although it's never explicitly stated, the intent seems to be that every weapon either requires 1 or 2 hands to wield, so any handheld weapon that isn't two-handed must be one-handed.
(This answer was adapted from my answer to another question.)