Here are various statements that Swaminarayan makes about Shiva in the course of the Vachanamrut, a central scripture of the Swaminarayan sect:
In Gadadha 1-23 of the Vachanamrut, Swaminarayan gives Shiva as an example of a devotee of Vishnu who still identifies himself with the body:
There are two types of Bhaktas of Bhagavan: One Bhakti has complete Nischay in Bhagavan, yet worships Bhagavan identifying himself with the body. The other, believes his own Svarup to be Chaitanya, and beyond the influence of the three mental states and the three bodies.... Such is the Stithi of this Bhakta. As long as a person has not attained this Stithi, he is subject to obstacles, even if he is a Bhakta of Bhagavan. For example, Shivji did not have this Stithi and was therefore enticed by the beauty of Mohini.
In Loya 1 of the Vachanamrut, Swaminarayan says that even though he does not have Bhakti towards Shiva, he still has great respect for Shiva as a fellow devotee of Vishnu:
Last night, an hour or two before sunrise, Shivji granted me his darshan in a dream. He was seated on the big, powerful Nandishvar. His body was of a large build, and he had thick, matted hair; he appeared to be approximately forty years of age. Along with Shivji was Pãrvati, who was wearing all white clothes. Shivji, like a great sãdhu, appeared tranquil, and he showed great love towards me. However, I did not feel love for him. This is because I believe, ‘Shiv is a dev that is full of tamo-gun, whereas I worship Shree Krishna-Narayan who is the incarnation of tranquillity’. Therefore, I do not have much love for devs like Brahma, Shiv, and Indra, who have rajo-gun and tamo-gun. Moreover, I have much hatred towards anger; I do not like angry men or angry devs. Nonetheless, why do I respect Shivji? I do so because he is a Tyagi, a Yogi, and a great Bhakta of Bhagavan.
In Loya 11 of the Vachanamrut, Swaminaryan says that those who seek Moksha should not meditate upon Devas like Brahma and Shiva:
Specifically, those desiring Kalyan should not perform dhyãn upon – with the exception of Purushottam Narayan – any devs, such as Shiv and Brahmã. Instead, among all humans and devs, they should perform dhyãn only upon murtis, such as Rãm and Krishna, which are avatãrs of Purushottam Narayan.
In any case, I think out of all the Vaishnava sects, the Pushtimarga sect and the Gaudiya Vaishnava sect give Shiva the highest status. Most Vaishnava sects consider Shiva to be the greatest Vaishnava, but Vallabhacharya's Pushtimarga sect goes one step further and calls him the "first Vaishnava", because they consider him to be the first Acharya in their Guru Parampara. And then Chaitanya Mahaprabhu's Gaudiya Vaishnava sect goes even beyond that and accords Shiva a status nearly equal to that of Vishnu; they believe there's a category above Jiva-Tattva and below Vishnu-Tattva called Shiva-Tattva.