I suppose the way to do it is easy. Either he charges at the Takeda to save generals who were trapped, rather than being convinced by others to retreat back to Hamamatsu, this being a...different Ieyasu Tokugawa to the man we know, or is killed during the retreat. If morale isn't broken utterly by his non-showing, it's likely that Hamamatsu will shut the gates and ready for siege rather than go for an open-castle bluff, a siege that the Takeda will likely smash through.
Now, I think the Takeda could still withdraw. The vanguard would most probably remain free from ambush ITTL, yes, but it's still Winter, Shingen may still die, and the Uesugi would be testing the borders in the crab-bucket nature that made it difficult for many Daimyo to really March on Kyoto. With that is the question of what happens to the Matsudaira/Tokugawa. Nobunaga had the Azai and Asakura on the back-pedal after Anegawa easily, and the sieges were more them buying time before they'd die. With the issue of succession and the death of one of the few people he had unconditional affection for, however he may delegate leading the siege to a retainer, as he focuses on the task of dealing with the Matsudaira succession and threat of the Takeda.
Matsudaira Nobuyasa is Ieyasu's oldest son at the age of fourteen, married to Nobunaga's oldest and favourite daughter, so it's likely that Nobunaga will 'suggest' that they follow the traditional rules of succession. Nobuyasa IOTL was later made to commit seppuku in 1579 in suspicion of an anti-Oda plot, in Nobunaga's more...eccentric moments, which was not too contested which may reflect his later unpopularity or fear of Nobunaga. Either way, the Matsudaira will likely more answer to a group of trusted retainers and friends of Ieyasu.
In an ideal Oda scenario, this arrangement works out and Shingen dies a similar death as IOTL when he invades Noda Castle, the Azai and Asakura can safely be smashed, and the Oda-Matsudaira alliance will likely be a clear senior-junior alliance wherein Nobuyasa is as much a vassal as he is an ally, rather than the OTL one where there was a bit more equality, trust, and friendship involved. If Nobuyasa complains, then his potential unpopularity as IOTL will see him replaced with either a son born ITTL or Yuki Hideyasu (but actually retainers wanting a less difficult master). Ideal Takeda would be the opposite, the Matsudaira collapse, Shingen survives, Nobunaga has to make peace and direct resources, is beaten back by Shingen, and smashed between his enemies. Shingen makes it to Kyoto, and becomes Shogun.
I'd say the result will be in the middle. The Matsudaira will never have the stability and firm loyalty they had IOTL, with Ieyasu as the linchpin, but the martyr factor will probably be enough for them to stand and fight when the Takeda strike. As to Shingen's success, it depends on which death-theory you buy into. If it's a sniper, then the butterflies may save him, or doom him in a future battle in the campaign. Luck was a large part of these times, especially for Nobunaga, Ieyasu, and even Shingen, and it may be that Takeda enjoys it this time. Pneumonia, on the other hand, probably won't be stopped by Ieyasu dying.
Ieyasu's reputation is sunk, however. He might redeem himself if his death was fighting to the last, saving those he doomed, but if he dies on the retreat then he's sunk. His generals, the help Nobunaga sent, and even a letter from Nobunaga himself, all said that he should hole up in Hamamatsu. Either the Takeda move on and expose themselves to attack, have to divert resources, or get stuck in a siege. Ieyasu rejected all the advice and moved to fight Shingen in open battle, as was his style back then, the crushing defeat at Mikatagahara changing him to the more cautious figure we know today. Another lesser warlord, cut down by Shingen Takeda's skill in warfare and his own failings.
EDIT: Actually, my mistake, Yuki Hideyasu was born after Mikatagahara. Not to mention that Ieyasu only had half-brothers and half-sisters, which means that if Nobuyasa doesn't have a son between succeeding (if he even does, assuming Shingen dies) and his wife and mother's feud, he might be safe. If the Takeda manage to beat down the Matsudaira, and manage to defeat Nobunaga, then the whole point is moot.
If Hideyasu's mother is made to commit seppuku as a result of his wife's actions, and not him, we might see a few changes.