The most important fact about this question is the stereochemistry of nitrosyl chloride $(\ce{NOCl})$ addition to an alkene. The OP has wondered whether it follows syn- or anti-addition.
The answer is not simple one word answer. According to the Ref.1, the nitrosochlorination of alkenes is shown to possess features common to other reactions of electrophilic addition, yet the stereochemistry of the addition depends on the structure of the alkene. For example, the addition of $\ce{NOCl}$ to norbornene follows cis-stereochemical course while that to $\Delta^9$-octalin follows trans-stereochemical course. However, the Ref.2 suggests that stereochemical outcome of the reaction also depends upon solvents used in the reaction. For instance, the stereochemistry of the addition of nitrosyl chloride to cyclohexene in liquid sulfur dioxide is not the same when the identical reaction is performed in $\ce{CH2Cl2}$ or in $\ce{CHCl3}$ (Ref.2).
In later studies of same reaction in liquid sulfur dioxide, the trans-stereochemical out come of the dimeric product has established by NMR spectral data (Ref.3).
Structural influence on this reaction was also established on the $\ce{NOCl}$ addition on 3,4,6-tri-O-acetyl-D-glucal, which has predominantly showed cis-addition (Ref.4 & 5):

The structural effect is also evedence in oxymercuration: The oxymercuration of D-glucal has given the corresponding cis-product while that of its 3,4,6-triacetate has given the corresponding trans-product (Ref.6).
References:
- P. P. Kadzyauskas and Nikolai S. Zefirov, "Nitrosochlorination of Alkenes," Russian Chemical Reviews 1968, 37(7), 543 (DOI:
https://doi.org/10.1070/RC1968v037n07ABEH001665).
- Masaji Ohno, Masaru Okamoto, and Kenkichi Nukada, "Dependence of steric course of nitrosyl chloride addition to cyclohexene on solvents," Tetrahedron Lett. 1965, 6(45), 4047-4052 (DOI: https://doi.org/10.1016/S0040-4039(01)99612-1).
- B. W. Ponder, Thomas E. Walton, and William J. Pollock, "Addition of nitrosyl chloride to cyclohexene," J. Org. Chem. 1968, 33(10), 3957-3959 (DOI: https://doi.org/10.1021/jo01274a065).
- R. U. Lemieux, T. L. Nagabhushan, and S. W. Gunner, "Synthesis of 3,4,6-Tri-O-acetyl-2-oximino-α-D-hexopyranosides," Can. J. Chem. 1968, 46(3), 405-411 (DOI: https://doi.org/10.1139/v68-06).
- R. U. Lemieux, T. L. Nagabhushan, and I. K. O'Neill, "A new approach to the synthesis of 2-amino-2-deoxyglycosides," Tetrahedron Lett. 1965, 5(29), 1909-1916 (DOI: https://doi.org/10.1016/S0040-4039(01)89472-7).
- Philip T. Manolopoulos, Morton. Mednick, and Norman N. Lichtin, "Oxymercuration of D-Glucal and Its 3,4,6-Triacetate," J. Am. Chem. Soc. 1962, 84(11), 2203–2210 (DOI: https://doi.org/10.1021/ja00870a036).