The applicable NEC cite for a typical air handler of this nature is 424.19(A)(2) (424.19(A)(1) does not apply to most air handlers as the fan motor in them is over 1/8 HP):
424.19 Disconnecting Means. Means shall be provided to
simultaneously disconnect the heater, motor controller(s),
and supplementary overcurrent protective device(s) of all
fixed electric space-heating equipment from all ungrounded
conductors. Where heating equipment is supplied by more
than one source, feeder, or branch circuit, the disconnecting
means shall be grouped and marked. The disconnecting
means specified in 424.19(A) and (B) shall have an ampere
rating not less than 125 percent of the total load of the
motors and the heaters and shall be lockable in accordance
(A) Heating Equipment with Supplementary Overcurrent Protection. The disconnecting means for fixed electric
space-heating equipment with supplementary overcurrent
protection shall be within sight from the supplementary
overcurrent protective device(s), on the supply side of these
devices, if fuses, and, in addition, shall comply with either
424.19(A)(1) or (A)(2).
(2) Heater Containing a Motor(s) Rated over 1/8 Horsepower. The above disconnecting means shall be permitted
to serve as the required disconnecting means for both the
motor controller(s) and heater under either of the following
(1) Where the disconnecting means is in sight from the
motor controller(s) and the heater and complies with
Part IX of Article 430.
(2) Where a motor(s) of more than 1/8 hp and the heater are
provided with a single unit switch that complies with
422.34(A), (B), (C), or (D), the disconnecting means
shall be permitted to be out of sight from the motor
Given that the motor controller in an air handler is going to be inside the air handler (it's the fan relay there), unless your air handler has a unit switch on the outside to serve as a disconnecting means, then you need a motor-rated disconnecting means in sight of the air handler. A non-fusible molded case disconnect like the one you linked works; you can also use a breaker-based "spa panel" type disconnect like the ones used for air conditioners provided the current rating is suitable, or even a subpanel if you wish to run the serviceman's receptacle and whatnot off the same set of wires as the air handler.
Also, having a door on a cabinet or cutout box does not violate "readily accessible" under the 2017 NEC:
Accessible, Readily (Readily Accessible). Capable of being reached quickly for operation, renewal, or inspections
without requiring those to whom ready access is requisite
to actions such as to use tools (other than keys), to climb over or remove
obstacles, or to resort to portable ladders, and so forth.
Note: Use of keys is a common practice under controlled or supervised conditions.