Ziyarat e Ashura is a mustahhab act and there is no compulsion in reciting the salam and laan 100 times. If one doesn't have time, he can recite just once. There are other options too:
1. Reciting 100 times just the last part of that paragraph and not the entire paragraph i.e "Allahumalan Jamian" «اللهم العنهم جميعا» and reciting 100 times just the last part of the salam and not the entire paragraph of salam i.e "As salamu alal Husain va ala ali ibnil Husain va ala avladil Husain va al ashabil Husain" «السلام علي الحسين و علي علي ابن الحسين و علي اولاد الحسين و علي اصحاب الحسين»
2. One can also recite 100 times the entire paragraph throughout the day. Its not compulsory to recite in one sitting.