WGS 1984 has had several "releases". I'm not sure whether or not to call them re-adjustments. WGS 1984 is loosely tied to the International Terrestrial Reference Frame (ITRF), maintained by IERS.
The first transformation, WGS_1984_(ITRF00)_To_NAD_1983, assumes that WGS 1984 is the one tied to ITRF00 and the NAD 1983 realization is CORS96 or similar. That version is also known as WGS 1984 (G1150). The current realization is WGS 1984 (G1674) which is related to ITRF08 instead. This transformation uses the non-time-related parameters from the NGS CORS website. They've since published a new transformation relating ITRF08 and NAD 1983 (2011), which Esri has as WGS_1984_(ITRF08)_To_NAD_1983_2011.
NGS has released, as beta, grid file-based transformations between "HARN" and NSRS2007, GEOCON, and between NSRS2007 and NAD 1983 (2011), GEOCON11. They do include Alaska. Esri has not incorporated them yet into the software. The GEOCON/GEOCON11 file format and interpolation method differs from previous NGS file formats and interpolation methods. Their beta version only accepts Blue Book-formatted data as well.
The 2nd transformation you list assumes WGS 1984 is ITRF96, so it's quite old compared to the other two. EPSG has either deprecated it, or lists the extent as excluding Alaska, but Esri has customers there using it which is why Esri lists it as covering Alaska too.
So for now, I"m not sure what to tell you. I think I would recommend WGS_1984_(ITRF00)_To_NAD_1983 as closest to NSRS2007.
Disclosure: I work for Esri.
Typically, NAD83 and WGS84 are within one meter of each other. Your concerns about differences of 2.5 feet, which are less than a meter, indicate you do need to perform this datum transformation.
Briefly, this calculation requires knowledge of when the coordinates were collected so that their movement over time can be accounted for (primarily due to the movements of underlying tectonic plates and partly due to "episodic motion associated with earthquakes"). You first convert the raw data to equivalent coordinates referenced to specific standard dates, such as 1997.0 or 2002.0. Then you look up 14 parameters describing (a) the offset, rotation, and rescaling (i.e., a seven-parameter transformation) needed to change datums at a given date together with (b) the first derivatives of those parameters with respect to time. Multiplying (b) by the elapsed time and adding to (a) gives a first-order approximation to the needed seven-parameter transformation, which you then apply.
Although the procedure is not mathematically difficult, it is rather involved and contingent on details of how your data were originally collected and processed. An NOAA paper, Transformations Between NAD83 and WGS84, provides a clear, readable explanation. It recommends you use interactive "Horizontal Time-Dependent Position" software, HTDP, available on the NOAA Website at http://www.ngs.noaa.gov/TOOLS/Htdp/Htdp.shtml. The Fortran source code consists primarily of the coefficients of the plate tectonic model plus some interface code, but I estimate around 3,000 lines actually do calculations. It could be a significant pain to port.
Best Answer
Short answer is yes. You need to convert from your coordinates' native reference frame to the NAD83 realization's reference frame, then possibly add an adjustment. In the case of NAD83(CSRS), which I use, there are 3 steps:
Steps 1 and 2 require the Helmert transformation. Step 3 uses interpolated shifts from a raster to apply adjustments due to tectonic motion and isostatic rebound.
NAD83 is intended to be locked to the North American plate so its realization must rotate with respect to the reference frame. In CSRS this accounted for partly by the final reference frame transformation and partly by the grid shift. (It's fairly difficult to find complete information on this online -- when I was writing software to transform point clouds, I had some generous help from the NRCAN scientist who's responsible for it.)
The IERS publishes transformation parameters for going between various ITRF realizations: here.
I got the ones for CSRS from The Evolution of NAD83(CSRS) In Canada, by Mike Craymer (2006). This page has the transformation parameters between 2011 and ITRF. (This one has a spreadsheet with many transformations.)