No, he/she should not conceal the fact that they are Jewish. When you do this, you say that you worship men more than you worship God. The Jewish people are called to be a nation of priests to the whole world, and we are commanded to wear certain clothing to illustrate this point. It's understandable that there will be certain points at certain times where you will fall short of this ideal, and you will have sinned against God. But the moment that you become more worried about how others will perceive your sin, rather than being worried about the fact that you sinned against God, you have a much bigger problem. Because you are worshiping men, rather than worshiping God.
It has become commonplace to view tzit tzit or kippot as outward expressions of ones being Jewish. Rather than their actual purpose, which is to remind us of God's commandments, anywhere at anytime, especially when we are sinning. A practical example will be that one will be afraid to be seen wearing a kippah at a McDonalds in which he is grabbing a coke (which is permissible), but feels no remorse about actual sins in which no one is looking at him. Rather than this hypocrisy, one should embrace their Judaism at all times, and all moments, using it as a force toward holiness and repentance to God.
A great example of this is brought down in the Talmud in Menachot 43b-44a
Once a man, who
was very scrupulous about the precept of zizith, heard of a certain harlot in one of the towns by the sea who accepted four hundred gold [denars] for her hire. He sent her four hundred gold [denars] and appointed a day with her. When the day arrived he came and waited at her door, and her maid came and told her, ‘That man who sent you four hundred gold [denars] is here and waiting at the door’; to which she replied ‘Let him come in’.
When he came in she prepared for him seven beds, six of silver and one of gold; and
between one bed and the other there were
steps of silver, but the last were of gold. She
then went up to the top bed and lay down
upon it naked. He too went up after her in his
desire to sit naked with her, when all of a
sudden the four fringes [of his garment]
struck him across the face; whereupon he
slipped off and sat upon the ground.
She also slipped off and sat upon the ground and said,
‘By the Roman Capitol, I will not leave you alone until you tell me what blemish you saw in me. ‘By the Temple’, he replied, ‘never
have I seen a woman as beautiful as you are; but there is one precept which the Lord our God has commanded us, it is called zizith,
and with regard to it the expression ‘I am the
Lord your God’ is twice written, signifying, I
am He who will exact punishment in the
future, and I am He who will give reward in
the future. Now [the zizith] appeared to me
as four witnesses [testifying against me]’.
said, ‘I will not leave you until you tell me
your name, the name of your town, the name
of your teacher, the name of your school in
which you study the Torah’. He wrote all this
down and handed it to her. Thereupon she
arose and divided her estate into three parts;
one third for the government, one third to be
distributed among the poor, and one third
she took with her in her hand; the bed
clothes, however, she retained. She then came
to the Beth Hamidrash of R. Hiyya, and said
to him, ‘Master, give instructions about me
that they make me a proselyte’.
daughter’, he replied; ‘perhaps you have set
your eyes on one of the disciples?’ She
thereupon took out the script and handed it
to him. ‘Go’, said he ‘and enjoy your
acquisition’. Those very bed-clothes which
she had spread for him for an illicit purpose
she now spread out for him lawfully. This is
the reward [of the precept] in this world; and
as for its reward in the future world I know
not how great it is.
Rather than taking off his tzit tzit when he was on his way to the prostitute, he kept them on. Rather than hiding the fact that he was Jewish when he realized he was sinning, he made it very clear that he was Jewish, and even explained the Judaism to a gentile, and the world was made better for it.