Should do just fine. My cousins mother-in law(we call her Mrs. elk-whacker) only uses one rifle for all her hunting....35 Rem. with -I think-200gr round nose bullets. In the past 4 years she's only drawn an elk tag twice and was successfull both times. They were cows. She loves her ''gun''
I would prefer the Whelen but wouldn't be afraid of using the 35 Rem. Your range is going to be limited but you should have plenty of power. My Dad has been hunting with a 35 Whelen improved for more than 20 years. He's killed a pile of elk with it in mostly short range conditions.