She cannot take off her hijab when doing wudoo’ at work; should she wipe over it?

Firstly: 

It seems that it is difficult for you to take off your hijab
because of the presence of non-mahram men in your workplace. If that is the
case, then you should note that mixing of women with non-mahram men leads to
many negative consequences, such as being alone with or looking at a member
of the opposite sex, speaking softly, temptation, and other things that are
no secret to people of insight. Please see question no.
1200 for evidence
that free mixing is haraam. 

Secondly: 

If a woman is faced with this problem and the time for prayer
comes whilst she is at work, and she cannot delay it until she goes back
home, then she should pray in the most concealed place in her workplace,
covering her hands, face and all of her body in front of non-mahram men. We
have already stated this in the answer to question no.
39178 . 

Thirdly: 

Your saying that it is difficult to take off your hijab in
order to wipe your hair and ears when doing wudoo’ makes us wonder: how do
you wash your arms and feet in the presence of men? 

You must be aware that the arms and feet are part of the
‘awrah which must be concealed from non-mahram men. As for the face and
hands, there is some difference of scholarly opinion, but the most correct
view is that they must also be covered. See question no.
11774. 

Fourthly: 

It is permissible for a woman to wipe over her khimar (head
cover) in the case of necessity, such as when it is very cold, or it is
difficult to take off her hijab and put it back on. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was
asked: It is permissible for a woman to wipe over her khimaar? 

He replied: 

The well known view in the madhhab of Imam Ahmad is that she
may wipe over her khimaar if it goes under her chin, because it was narrated
that some of the womenfolk of the Sahaabah (may Allaah be pleased with them)
did that. 

Whatever the case, if
there is some difficulty, either because the weather is cold or because it
is difficult to take it off and put it on again, then there is nothing wrong
with wiping in such cases, otherwise it is better not to do that. End
quote. 

Fataawa al-Tahaarah, p. 171 

It says in Sharh Muntaha al-Iraadaat (1/60): It is
also valid for a woman to wipe over a khimaar that goes under the chin,
because Umm Salamah used to wipe over her khimaar, as was mentioned by Ibn
al-Mundhir. End quote. 

So long as the khimaar covers the ears, it is sufficient to
wipe over the khimaar and there is no need to put the hands under the
khimaar to wipe them. Similarly, if a man is wearing a turban, he does not
have to wipe his ear too, even if they are not covered; rather that is
mustahabb only. 

Shaykh Ibn ‘Uthaymeen
(may Allaah have mercy on him) said: It is also Sunnah to wipe whatever part
of the head is uncovered, such as the forelock, the sides of the head and
the ears. 

Fataawa al-Tahaarah, p. 170 

Fifthly: 

A Muslim woman must strive to fear Allaah and obey His
commands, and avoid that which He has forbidden, and keep away from working
in mixed environments, which may earn her the wrath of Allaah. She should
beware of giving this world precedence over the Hereafter, for it is
transient pleasures, but what is with Allaah will never fade away. It is
narrated in a saheeh report that our Prophet (peace and blessings of
Allaah be upon him) said: “Whoever gives up a thing for the sake of Allaah,
Allaah will compensate him with something better than it.” Classed as saheeh
by al-Albaani in Hijaab al-Mar’ah al-Muslimah, p. 49. 

We ask Allaah to help you to do that that which is best for
you in this world and in the Hereafter. 

And Allaah knows best.