Warlock with Wand +1 and shield (hexblade, he has proficiency in shields)
A spellcaster must have a hand free to access a spell's material components—or to hold a spellcasting focus—but it can be the same hand that he or she uses to perform somatic components (PHB p.203)
Can he cast spells that need S component but not M? (without warcaster feat)
According to the Sage Advice Compendium referenced in this answer state that you can only use the hand holding your focus if the spell requires a non-costly material component.
This seems to make no sense and is likely one of those rulings from the devs that I will ignore as illogical. There is seemingly no difference between somatic components between a spell that requires material components and one that doesn't. There is nothing breaking in this decision at all. Most of us hand waive over the free hand to a certain extent anyway. The SA ruling seems to be overly punishing.
In short: No you can't, you still need that free hand
When casting spells you typically need 1, 2 or all 3 types of component: Material, Somatic, and Verbal. Spells that require a verbal component only require the use of your mouth, however Somatic and Material components require a free hand:
PHB 203
Somatic (S)
Spellcasting gestures might include a forceful gesticulation or an intricate set of gestures. If a spell requires a somatic component, the caster must have free use of at least one hand to perform these gestures.
Material (M)
….. A spellcaster must have a hand free to access these components, but it can be the same hand that he or she uses to perform somatic components.
A shield does take the use of one of your hands as does the Hexblade. For Hexblade Warlocks, the Hexblade can't be used a spellcasting focus nor is any indication given that you can perform Somatic components while holding the Hexblade in your hand. Looking into Warlocks further I found no evocations or class abilities that would allow any similar effect to what you are looking for.
