Non-halogen intermediate between alkane and alcohol under basic conditions?
I think that you're asking if there is a way to convert an alkane to an alcohol without using halogens in the process.  

Alkanes are relatively unreactive and so high energy species (like free radicals) are most often used to carry out reactions on alkanes. The  reaction of alkanes with halogens that you've mentioned is an example of this free radical process.

Other high energy molecules that can be used to convert alkanes to alcohols include ozone and (photo-) chemically generated singlet oxygen.  Just like with the halogens, these reactive molecules show little selectivity, so if primary, secondary and tertiary hydrogens co-exist in your alkane, then a mixture of primary, secondary and tertiary alcohols result.  However in molecules such as cyclohexane, where there is only one type of hydrogen, somewhat useful results can be obtained.  I say "somewhat useful" because ozone and singlet oxygen can oxidize the resultant alcohol further to a carbonyl.  Here is a reference to an abstract on the use of ozone to functionalize alkanes.  

Reagents such as potassium permanganate and chromic acid also oxidize alkanes by a free radical mechanism to produce alcohols.  Again the issues of selectivity and further oxidation remain.

Here is a link to a nice review entitled "Alkane Hydroxylation." It covers a wide variety of reagents.  Most of the molecules depicted contain functional groups which can help improve selectivity, but there are a number of hydrocarbon examples as well.  Perhaps you'll find an example that is similar to your molecule of interest.