ば - most commonly used たら - can be used, but is less common なら - only in limited contexts *と - unacceptable
ex：君さえ承知してくれたら・(してくれる）なら、今すぐこのプロジェクトを始めるつもりだ。 As long as you agree (to our plan), we are planning to begin this project right away
In the example, 何の迷いもなく到着します does not make sense. It should be 迷わないで到着できたのに(we would have gotten to our destination without going astray). 迷いもなく is okay, but normally it is used to describe abstruct mental confusion rather than physical or concrete one.
sentence pattern "sae..ba"= coditional sentence type III???