Having taken all those factors on board, you need to decide your start point- there are several options, all with pros and cons. You can also do the traverse in the opposite direction, but that is slightly more tricky as you have awkward pinnacles on the Dom ridge to descend in this direction, as well as the harder descent of the S ridge of the Täschhorn. Described here you have the highest starting point, from the Mischabeljoch bivouac hut, allowing the quickest traverse, giving a degree of extra safety, as well as the easier descent from the Dom down the glacier.

Follow the standard route from the bivouac hut up the S Ridge of the Täschhorn. From the summit descend slabby rock, tricky if icy, with poor protection, going round a rocky tower on its R. Easier ground leads to the lowest point, the Domjoch at 4281m. The rock beyond here is bad so be particularly careful and sure footed. Another gendarme of poor rock is turned on its R, then there's a level section before the final rocky steepening. Luckily the rock improves here and leads to the summit of the Dom. Breathe a sigh of relief, grab a bite to eat and a drink then track down the glacier on the normal route, leading to the Dom Hut.