Both sharks and dolphins have been known to live in and around India. The Irrawaddy dolphin and the Ganges shark are species that actually live in seas or swim up rivers. It seems like there should be some mention of either of these creatures in Hindu mythology.
So are there any references to them in scriptures?
Yes many aquatic species are mentioned in the texts including doplhins, sharks, turtles and whales. The Dolphin (or Śiśumāra) is in fact associated with many gods including Varun, the Lord of the Ocean & Shri Krishna/Vishnu:
Vaman Puran Chapter 9 Verse 17 (Page 44 in this document) mentions:
Śiśumāra called jaladhi is the carriage of Varuna. It was originated from the ear wax of Rudra. It has dark complexion and divine speed.
Srimad Bhagavatam Canto 5 Chapter23 refers to the shape of our coiled galaxy to be similar to that of a dolphin and calls it a manifestation of Lord Krishna:
SB 5.23.4: This great machine, consisting of the stars and planets, resembles the form of a śiśumāra [dolphin] in the water. It is sometimes considered an incarnation of Kṛṣṇa, Vāsudeva. Great yogīs meditate upon Vāsudeva in this form because it is actually visible.
SB 5.23.5: This form of the śiśumāra has its head downward and its body coiled. On the end of its tail is the planet of Dhruva, on the body of its tail are the planets of the demigods Prajāpati, Agni, Indra and Dharma, and at the base of its tail are the planets of the demigods Dhātā and Vidhātā. Where the hips might be on the śiśumāra are the seven saintly sages like Vasiṣṭha and Ańgirā. The coiled body of the Śiśumāra-cakra turns toward its right side, on which the fourteen constellations from Abhijit to Punarvasu are located. On its left side are the fourteen stars from Puṣyā to Uttarāṣāḍhā. Thus its body is balanced because its sides are occupied by an equal number of stars. On the back of the śiśumāra is the group of stars known as Ajavīthī, and on its abdomen is the Ganges that flows in the sky [the Milky Way].
SB 5.23.6: On the right and left sides of where the loins might be on the Śiśumāra-cakra are the stars named Punarvasu and Puṣyā. Ārdrā and Aśleṣā are on its right and left feet, Abhijit and Uttarāṣāḍhā are on its right and left nostrils, Śravaṇā and Pūrvāṣāḍhā are at its right and left eyes, and Dhaniṣṭhā and Mūlā are on its right and left ears. The eight stars from Maghā to Anurādhā, which mark the southern course, are on the ribs of the left of its body, and the eight stars from Mṛgaśīrṣā to Pūrvabhādra, which mark the northern course, are on the ribs on the right side. Śatabhiṣā and Jyeṣṭhā are on the right and left shoulders.
SB 5.23.7: On the upper chin of the śiśumāra is Agasti; on its lower chin, Yamarāja; on its mouth, Mars; on its genitals, Saturn; on the back of its neck, Jupiter; on its chest, the sun; and within the core of its heart, Nārāyaṇa. Within its mind is the moon; on its navel, Venus; and on its breasts, the Aśvinī-kumāras. Within its life air, which is known as prāṇāpāna, is Mercury, on its neck is Rāhu, all over its body are comets, and in its pores are the numerous stars.
This form is again compared to that of Lord Vishnu:
SB 5.23.8: My dear King, the body of the śiśumāra, as thus described, should be considered the external form of Lord Viṣṇu, the Supreme Personality of Godhead. Morning, noon and evening, one should silently observe the form of the Lord as the Śiśumāra-cakra and worship Him with this mantra: "O Lord who has assumed the form of time! O resting place of all the planets moving in different orbits! O master of all demigods, O Supreme Person, I offer my respectful obeisances unto You and meditate upon You."
SB 5.23.9: **The body of the Supreme Lord, Viṣṇu, which forms the Śiśumāra-cakra, is the resting place of all the demigods and all the stars and planets. **One who chants this mantra to worship that Supreme Person three times a day — morning, noon and evening — will surely be freed from all sinful reactions. If one simply offers his obeisances to this form or remembers this form three times a day, all his recent sinful activities will be destroyed.
In the Bhagvad Geeta 10.31 Shri Krishna mentions that he is a shark among the fishes:
पवन: पवतामस्मि राम: शस्त्रभृतामहम् | झषाणां मकरश्चास्मि स्रोतसामस्मि जाह्नवी || 31||
pavanaḥ pavatām asmi rāmaḥ śhastra-bhṛitām aham jhaṣhāṇāṁ makaraśh chāsmi srotasām asmi jāhnavī
Of purifiers I am the wind; of the wielders of weapons I am Rama; of fishes I am the shark, and of flowing rivers I am the Ganges.
Other aquatic animals are also mentioned in Ramayana especially in the Yuddha Kand:
caNDa makra graham ghoram kSapaa aadau divasa kSaye | hasantamiva phenaughairnR^ityantamiva cormibhiH || 6-4-113
Rendered appalling by the ferocity of fierce alligators and crocodiles, that ocean with its foaming waves at the end of the day and at the beginning of the night, appeared to laugh and dance.
candra udaye samaadhuutam praticandra samaakulam | caNDa anila mahaagraahaiH kiirNam timi timimgilaiH || 6-4-114
The ocean surged, when the moon rose. The image of moon was reflected limitlessly in it. The sea was full of huge alligators swift as fierce winds along with whales and great whale-eating fish.
Therefore, to conclude yes these as well as other aquatic animals are mentioned in the scriptures.
In the Bhagavadgita 10 .31
Krishna says
Of purifiers I am the wind, of the wielders of weapons I am Rāma, of fishes I am the shark, and of flowing rivers I am the Ganges.
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