On par mechanically, but lacking thematically.

tl;dr Stat bonus probably makes up for the underwhelming attack versatility and cantrip addition.

The comparable feats that come to mind are artificer initiate, crossbow expert, magic initiate, and war caster

Attack versatility

The comparable feats all grant attack versatility in the form of additional cantrips, or being able to use a ranged attack in an additional way.

• additional cantrips
• additional attacks (ignore loading, bonus action attack)
• attack versatility (up close, attacks of opportunity)

The proposed feat actually comes across as slightly under powered with respect to an mechanical increase in attack. Only granting a single cantrip with restrictions, and a minor added versatility of attacking within 5' without penalty is less good than the other martial or magical feats.

Ability Score Increase (ASI)

None of the comparable feats give a stat bonus. This feat is tailored for wizards and artificers, so the add to their primary stat mitigates half the trade off of feat vs ASI. Given the niche use of ranged cantrips in the front line, the stat bonus is not an over reach.

Thematically nothing about this says wand but the title.

The initiate feats are about getting spells from a different class. The martial feats directly involve the implements of combat. There is nothing in the mechanics of this proposed feat that are tied or even about a wand.

Consider adding something like the warlocks pact weapon where the character can summon their wand to their hand as a free action, or must be using the wand as their spell focus in order to gain the up close benefit.