In reply to Gone for good: You only have two days and you want to climb a 4,000-m peak? You're not going to feel very well and normal routes on Mt Blanc 4000-ers do not generally go well in early spring, especially after a snowy winter - as this one has been. I think you would be advised to aim for shorter routes within easy access to a teleferique. There will be deep snow about - skis or snowshoes probably essential for approaches.
If you are a reasonably good rock climber (VS leader) the south facing Eperon des Cosmiques is ok at that time of year if it hasn't snowed. About five pitches, V or D- , abseil descent, walk back up to the Midi afterwards. The Cosmiques Arete (AD) will also be ok if it isn't too snowy and takes you to the top of the same mountain. On the north side the Mallory-Porter is about AD but a long way, around 1,000 m of climbing. It only has one tricky bit, a short mixed step. It does end at the top cable car station.
If you are confident on longer, slightly steeper snow and ice routes with a long descent then the Coutourier Couloir on the Verte (which is a 4,000-er) is possible. NB a long walk back to the valley after descending the Whymper to the Couvercle Hut. Do not try this if you have no previous Alpine winter experience. It's a big day out and you may encounter bullet hard ice near the top.
Other than that, there are plenty of somewhat more technical but less serious ice routes with equipped abseil descents. The Chere Couloir (D, Scottish 4) on the Tacul is an obvious choice. Other possibilities: N face of Col du Plan (AD+ or D, Scottish 3+) with descent from Midi 'frique; Petit Viking at the head of the Argentiere Glacier - longer and quite a bit steeper, maybe Scotish 4+ or easy 5.
If the snow is not too bottomless you might manage the normal route or the Y Couloir on the Aig. D'Argentiere, but you want to be very sure of snow and avalanche conditions.