I have very little time for shacharit, because I have to go to work. The minyan in the city where I live is very late. So I try to daven everything before the Amida and the Amida itself with a Tzibur, but after it I would like to skip and to cath up in the afternoon at my lunch break. The question is: What can I skip or, better, delay until later?
I'm not a rabbi, and this site makes no guarantee of validity. That being said,
- Tachanun is connected to the Amidah (the Rambam in fact considers it an aspect of the Amidah, Hil. Tefillah 5:13), so you should try to say it right afterwards.
- The kedusha verses of Uva Letziyon should preferably be recited with the congregation. I've heard that Aleinu is considered like asking permission to leave; according to this you should probably try to say it before leaving.
- On the other hand, the shir shel yom isn't necessarily part of Shacharis; on Tish'a Ba'av we push it off until Mincha. If you have to delay something, I'd suggest this.