Currently, none of the supported transformations for OSGB36 cover the Republic nor Northern Ireland. TM65_To_WGS_1984_2 is probably the best choice for conversion to WGS84 as the older transformations have no known accuracy values. 

You can find out about supported transformations in ArcGIS in [technical article 21327][1]. 

If the data's offshore, there's a transformation from OSGB36 to ED50 and you could then piece together other transformations. Accuracies are several meters.

You might check the online [EPSG Geodetic Parameter Dataset][2] to see if they have any other options. Note: I'm on the subcommittee that maintains the dataset. 

UPDATE - December 11 2017

EPSG:6946, TM75 to ETRS89 (3) (Esri name: "TM75_To_ETRS_1989_3_NTv2"), and EPSG:6947, TM75 to WGS 84 (4) (Esri name: "TM75_To_WGS_1984_4_NTv2"), were added to ArcGIS Desktop version 10.3.1. That version was released in mid-2015.


  [1]: http://support.esri.com/en/knowledgebase/techarticles/detail/21327
  [2]: http://www.epsg-registry.org