Alignment for predicting DNA hybridization?
As a rough and ready and very easy to perform test I would put the entire universe of dsDNA through Primer3 (details below). This could be done by "splicing" your probe of interest onto each "chunk" of dsDNA you pass through primer3 and restrict the primer search to the 20bp primer you are interested in. In other words you are forcing the program to consider the internal and trans-hybridisation of every possible dsDNA against your probe. If you probe is not recovered from a given search you would flag this on a subsequent parsing script and then that "chunk" of DNA would be assessed further. All the components required are in the link below. You would need to provide your own wrapper, but its fairly easy.

Primer3 will assess the internal thermodynamics of your probe and it has loads of options to assess the full range of behaviour, for example 3' hybridisation (which could be extended because you want 5' to 3'). It would be easy to construct a parameter grid around all the parameters of interest. Ultimately it would provide an additional layer of certainty, and everyone knows and trusts this algorithm (its also written in C, so its fast). 

The description of all the components is here , my specific purpose for customising the pipeline is different.



Bowtie2 will take a lot of RAM, I am not sure I would use it for this purpose, particularly if RAM is limiting (its used for genome assemblies against a reference). I'd ask the users whether Blat would be useful, because that is friendlier to the calculation you are performing. Anyway there some heavy duty Bowtie2 users around and their input would be useful.